New guy here.  I'm 71 and have a ton of experience with small engines.  A couple of years ago I bought a Simpson CM61083-S pressure washer, I believe on Amazon.  The reviews were very good, and the price/performance were very attractive relative to other offerings.  I have seen a post online that the engine, Simpson model CRX208cc, is copied from a Honda engine, and it does look for all the world like a Honda engine.  The first time I used it, I was totally amazed.  After I finished, as I always do, I turned off the fuel valve, let it run until the carb was empty, and siphoned the remaining gas from the tank.  The next time I used it was about 6 months later.  Filled it with fresh gas, turned on the fuel valve and pulled the cord about 50 times.  Nada.  Pulled the plug and checked for spark.  Next I filled a syringe with gas and squirted about 5 CC in the intake.  Sputtered for a few seconds.  Did it again, and after it started, just kept squirting gas until it would run on its own.  The engine was loping (rpm running up and down) a lot, like you would expect with stale gas. Not the case. I washed the garden tractor with it running like that for 10 minutes or so.  It maybe got a trifle better, but was never really happy and won't idle.   I'm thinking adjust the carb for probably a different blend of gas/ethanol, but can't find any adjustments.  
 
So, I decided to pull the carb and clean it just for kicks, knowing it wouldn't fix anything.  It was spotless and beautiful inside.  Looked like new.  Reinstalled it and it still runs the same.  I worked on a Craftsman pressure washer a while back for my brother-in-law that had the same symptoms.  It, too,  had the "not" adjustable carb.  I bought a new carb online for his and after installing it, it ran fine.  
 
It has been sitting around for over a year, and today I decided to try to do something with it again.  I see what I think is a correct carb on ebay, but this doesn't make any sense to me.  I don't understand what happened to a brand new carb after being used just one time, drained and properly taken care of.
 
Can anyone hold forth on this problem?  It doesn't make sense to chuck a brand new carb that should be working fine.  
 
I can't get the site to let me upload pictures, but, trust me, the carb looks pristine inside.
 
Best
 
Mike

There's one jet you likely missed... And it's SMALL..
 
Under the throttle stop screw is a black plastic thing.  Remove the screw and gently pry
out the plastic Jet (there may be another black plastic "spacer" above it -Save it for re-assembly)
 
Now with the last part out, you'll see a small brass insert with a hole..
 
That clog's up very easily.  I use a small vise grip, clamping a wire brush STRAND.
(Yes, it's that's small that my jet cleaning tool won't fit.)
 
Carb cleaner and gentle in and out with the wire.  That jet must be clear up into the hole.
carb cleaner when clean, will spray out the sides.  Do NOT try to punch ALL THE WAY THRU..
 
As a a side, should you have an engine surging, drilling open that jet, every so slightly with a jet drill bit, will richen the mix and get rid of the surge.  This is for engines with NO OTHER issues, just super lean from the factory...
 
.

Hi, Scott:
 
Well,  you were spot on.  Apparently you have seen this critter.  I didn't realize what that was.  That gives me a red face in 2 ways.  Back when I ran it the second time (when it was surging) as usual, I turned off the fuel and let it run until it quit.  I left the gas in, thinking I'd get back to it, and it has sat for nearly a  year.  I'm guessing that fuel shut off must let a little gas trickle through, as there was a little gunk in the carb this time.  Pulled both jets and gave it a good soak in lacquer thinner.  Sprayed carb cleaner through all the passages, cleaned the main jet thoroughly in carb cleaner, making sure all the little holes were clear, and cleaned that little mystery one you mentioned the same way.  Blew 70 PSI compressed air through every passage I could find, and the jets.  Have it back together now, but didn't arrive at happy land. 
 
Filled it with fresh gas, set the choke and it hit on the first pull.  Ran for a second and died.  Wouldn't hit again, choke or not no matter how much I pulled on it.  Pulled the drain plug from the carb and it is getting plenty of gas through the float valve.  Put that back and pulled it again.  Ran for a second.  Waited 5 minutes and it ran for a second.  After about a half hour of this routine, I found out that if I start it at about 1/2 throttle, it will run, but surges, sputters and misses out a lot.  Try to give it a little more throttle, no matter how gradually, and it dies instantly, like you turned it off.  Feels like the original problem, only worse.  This is what I expect when working on a carb with ADJUSTMENTS.....and set too lean.  Unfortunately, no adjustments.  
 
Starting to feel the price of a new carb slipping away.  I can afford it, but I can't buy one every time I want to use it.  Hate to impose further on your kindness, but do you have any more suggestions?  You seem to be familiar with this beast.
 
Best
 
Mike
 
 

Besides pulling the main jet, did you remove and clean the emulsion tube?
 
It's what just sticks up into the main venturi.  That also has very, very small holes that
must be clear.  You an gently push down from inside the venturi, then tap the carb  till it falls out..
 
Lastly, I know you have fuel at the carb.  Turn off (or clamp off) the fuel line and remove from the carb. 
Put a catch container under the hose, open the valve and make sure you have a good flow of fuel, NOT just a trickle...
 
.

Looking at a pic on-line a couple things.  Seems you have a fuel filter as part of the on/off fuel valve.
Remove that cup.  There's usually a screen inside there.  Make sure that clean and again fuel flows thru it when turned on..
 
Second, just for S & Gs, that machine has a low oil cut off switch.  It's not un-common for it to fail.
On the front of the engine is a sensor with one wire that plugs into the harness.  Simply un-plug it to 
disable it...  It's supposed to kill spark but when failing it often PARTIALLY KILLS SPARK.  It can have you chasing your tail....
 
..

Hi, Scott:
Concerning fuel, when I pull the drain plug on the carb, gas flows out of there plenty fast.  I'm very sure there is plenty of fuel flow to the carb.  "Emulsion Tube?"  I've never heard that term.  I have been mistakenly calling that the "main jet" all my life.  I did remove that and clean it very carefully.  
 
Again, I really do have a lot of experience on small engines.  It is the "not adjustable" thing that is killing me.  The engine acts like it is set too lean and is starving for fuel.  If it were adjustable, I would be turning the high jet screw open.  Is that little orifice you had me check earlier what regulates this?  It is marked 40V, I presume that means ".04 mm"?  What is that supposed to be called?  Apparently I need a little help with modern terminology.
 
I unhooked the oil sensor.  No help.  I put a couple tablespoons of Seafoam carb cleaner in the gas and ran it for about 10 minutes with the pressure hose disconnected to keep water going through the pump.  I very gradually increased the throttle a tiny bit at a time.  It sped up slightly each time, sputtering and surging the whole time until I nudged it ever so slightly more and it is like I shut off the ignition switch.  Just stops dead.
 
I think this makes the 3rd or 4th small engine with a non adjustable carb that I could not get working.  I'm wishing I could just put an older model carb on the darn thing.  I just went through all of this same crap with my brother-in-law's Craftsman pressure washer a couple of months ago.  Finally bought a carb and it was working when I left.  I don't know how many pennies the mfg saves by not installing the adjustments, but it is a TERRIBLE way to save them.
 
I'm going to jerk the carb and go through it again, but it won't matter.  I've been down this road several times, and I can smell defeat like a 4 day dead horse upwind.
 
I'll let you know what transpires.
 
Thanks a lot for the attempts to help.
 
Mike
 
 

Hi, Scott:
Went through that carb again.  I grabbed my bundle of old guitar strings and selected the best fits for each hole.  Roughed up the guitar strings with coarse sandpaper and worked the best fit through every orifice I could find, including all of those in that "emulsion tube".  I may have wallered out that one you told me about ever so slightly.  Blew everything out again with compressed air and put it back together.  As I suspected, absolutely no difference.  Ran it for 10 minutes again.  This is immensely frustrating.  What the heck can be wrong with that dang carb that I can't find????  Is there some passage somewhere I'm not finding??  
 
Misc observations:  Choke on, choke off, runs the same.  I can mostly block the intake with my fingers and it makes no difference.  On the side of the tank it states that the engine was tested with gasoline containing "ethanol shield" whatever that is.  I don't have any.  I have Stabil regular and marine formula, but can't imagine it would matter for this problem.  
 
While I'm waiting for any wisdom, I'm going to start searching the internet for a new carb.  I won't order one until I hear from you.  If I find one, I know it will fix the thing, because I've been down this road several times and it always does.
 
Again, thanks for your time.  Probably have too much angst, agony and labor in this to keep working on it.
 
Best
 
Mike

Hi, Scott:
I find carbs on the internet for $22ish plus shipping.  I also find this Honda carb (link below) that popped up in the same search and looks identical.  Any idea if it would work?  If so, would it be any better?  It is $42, but I'd gladly pop for it if it would help me avoid this trouble in the future.
 
Honda:  
 
Simpson:  Carb and complete tune up kit, only $22

 
 

Well, it didn't post the links.  Is that illegal?  I'll try again:
 
Simpson:  
 
Honda:  

Ok.  It won't post the links.  I'm just going to order the Simpson carb.  It comes with a complete tune up.  Unbelievable.  Spark  plug, ignition module, carburetor, fuel line, gaskets, on/off switch, fuel filter.  Holy cow.  $22?  How can they do that?
 
If you search for "Simpson CM-61083-S carburetor,  they are the first 2 results.  That Simpson carb sure looks exactly like the Honda carb....