358.791070 String Trimmer will not start

I am stuck. I have a 358.791070 trimmer which starts and runs for a few seconds and then dies. The 2 or 3 seconds that it runs is because I squirt fuel into the carb, set the choke, pull the starter a few times and it starts. I pull the trigger to increase rpm and it dies. It seems that there is no fuel from the carb going to the engine. I replaced the primer bulb, all fuel lines, the fuel filter on the end of the inline, the gasket between carb and engine. Same thing, nothing. It runs for a few seconds until the squirted in fuel is used up and then stops. So I figured I go for the sure fix (I thought) and ordered a brand new replacement carb Zama C1U-W32 (same what was in there) and nothing. Same symptoms. What am I overlooking? Can anybody help?

https://www.ebay.com/sch/...ster+tool&_sacat=0

Your applying a starter fluid and getting the engine to kick indicates it has spark..
 
You can pull the plug, check for the correct setting (about .025"), then crank over with the 
plug out and grounded to the engine.  You should(and likely will) see spark.
 
I've gotten some new carbs real close to the correct setting, some, not so much(especially the Chinese knock offs)..  
 
Just for yourself, once you have the tool, mark the handle.. Then WHILE COUNTING, turn each screw in and note if it's say 2 full turns in, 1.5, etc...Seat them LIGHTLY...      Just so you have a baseline..  
 
I suspect your compression is good as fuel(when applied) IS making it to the combustion chamber. A compression test wouldn't hurt. Pressure should be over 100PSI.
 
My moneys on those settings being set to lean..
 
*Also, it's not unusual for an engine to come in either not running or with a bad "bog" .
The settings are obviously set from the factory, as lean as possible.  Over time/use
they do need adjusting to RICHEN the mix up...
 
One other thing to check, which happens un-frequently, but does.  Look between the engine case and the cylinder.  There should be two bolts holding them together.  If you see ANY signs of dampness/black fuel dust where the parts meet, you have a leak.  Some machines use a gasket, some an o-ring..
You can just slip an allan key  or torx bit down to each screw and check for tightness...
 
Below is my Poulan I dis-mantled for a carbon clean up of the piston ring.  In the pic, you can see where the o-ring would sit as well as the two fasteners..
 

SRTs, I am still waiting for the adjustment tool. Do you know what the hole on the bottom of the carburetor is? You are looking at the side that mounts to the engine. There is also a hole like this on the engine side. What is that hole doing? I was trying to upload a picture to show you but I have not been able to do it. Strange why won't it let me upload a picture?
 
 

No, this one. See picture.

SRTs, that's good to know. Then you saw the pic. The hole circled in red on the engine side of the carb what is that hole? Is it the pulse line for the fuel pump or is fuel running thru that hole to the engine?

SRT, ok, but the hole that you circled in blue is on the side of the carburetor where the filter goes. The hole that I circled in red is on the side that attaches to the engine. Anyway if you don't know what that hole is that's alright. I did get the tools and I tried to adjust the carburetor and it started to run on its own, but no matter what I tried, it ran really crappy, but it ran beyond the squirted in fuel, so I was on the right track and I guess you were right about fiddling with the adjustments. Anyway I talked to the seller of the carb and he is going to send me a replacement. He thinks there might be something wrong with the carburetor itself. Hopefully the replacement carburetor will solve the problem. I will keep you posted.
In the meantime I overhauled the old carburetor just for the hell of it, because there is no reason why it shouldn't run. I replaced all the replaceable parts inside, but it still acts the same way. Then I noticed that the new carburetor has real good suction when I push the primer bulb and the bulb fills up nicely with fuel, but the old carb, which I so nicely overhauled has virtually no suction. I can pump the primer bulb but no gas gets into the bulb. What could cause that? Is there a leak somewhere inside, but where? Any idea?

SRT, Thanks for all your answers. The priming thing makes perfect sense. I am waiting for my new carb to come in. To bad this forum is not monitored or properly maintained by a staffer or administrator. When I look at my posts without being logged in (like you or anybody else would) my post #9 is gone picture and all. That's probably because it still says "Pending Approval". If I log in everything looks normal.