Ok HELP My Roper branded RT 13 has an ignition problem I cannot seam to solve and I'm at my witts end. I've rebuilt this machine and have way too much in to quit but I'm about to... So I lost spark at one point last year and replaced the condenser and points, then it lost spark again and I replaced the coil, then It lost spark again so I went back to the old condeser, after testing it, I figured the china junk wasn't working any more, old one tested out good new one was shot already after just a few runs, all good working again, washed it and lost spark again. WTF so I changed it all out to a new electronic coil no points or condeser required, started up and ran for about 15 minuted then made a horenous noise and died, pulled the head everything ok, but it was backfirring out the muffler so bad I thought it sucked in the exhaust valve, nope it sheared the flyway key and the timming was way off, replaced the key put it all back toegter for the umteenth time and it ran for a bout 20 minutes, set it to idle loaded my trailer with leaves, ran into the house to get a drink of water and as I stepped back out side it konked out, no problem just a restart, trottle it up and go again, nope, backfired out the exhaust really loud and some popping in the carburator, I take it apart again figuring its the keyway but it's fine? Hummmm.... Any help or suggestions greatly appreciated. I would replace the coil with a better quality one but have no way of telling the differnce between all the new ones out there, this is the one I have as suggested by a YouTube video but might not be right? So it's a 13 HP Briggs and Stratton.Model 302437 horizontal shaft motor. Open to suggestions... anything.

Do you have a strong spark?   If so, no use looking for another.  
 
You may want to check valve clearances at the back of the engine. 
 
And the flywheel key is still in place?
 
 
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/302400-to-302499/302437-0137-99 
 
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Ok I don't see my reply here so I am typing it in again. It has spark not so sure how strong it is but it back fires out the muffler with a good bang and pops in the carburetor as well, I can not imagine the valves have changed gap since it stalled out, I did pull the head and the valves were working properly and then it ran well again for 25 minutes or so, then it started misfiring again, the only thing I can figure is that the new electronic coil I choose is wrong somehow and I don't know how to research or verify it's the right one, or that it's working properly, I have tested the old coils and they tested OK but provided no spark, hence I thought it was the condenser again, points looked good, so I replaced the coil with the electronic coil to eliminate the points and condenser out of the equation and it worked like a charm until I sheared the flywheel keyway and then it worked agin until it stalled out while idling. I'd gladly replace the coils with a verified better quality one that fits the motor but I have yet to learn which one that might be. Yes I re-checked the keyway, it's good. I looked into the parts diagram but don't know how to find a cross reference number for a new electronic coil to replace this one. Thanks in advance for your help.
 

Sounds like something I might can help you with, post a picture of how the throttle cable hooks to the carb

Tight valves will get worse as the engine heats up.
 
Backfiring thru the exhaust and/or the intake indicates valves not closing fully 
or timing off.
 
If you won't check the valve clearances, which isn't hard to do, do a leak down test.
If there's leaky valves, etc, it'll show.  
 
Re the coil, there should be some markings on the coil that states "UP" when mounting.
The kill wire tab is usually on the bottom, closest to the block.
 
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Scott
I can check the valve clearances but that'll take some doings as there is a hood and carb in the way and lots of parts to come off to do it. If it's a warm up condition then it should start back up after a cool down, or a few days of not running? But I am willing to bet it won't start and the condition remains the same timing is off, but I will do those checks in the following days. Thanks
 
Coil is mounted correctly, I am aware of the magnet polarity and flipping of the coil if it's off rater than sending the flywheel out for polarity reversal and demagnetizing. Horizontal shaft engine, kill wire blade connector is towards the block behind the coil, I put an insulated connector on it and have repeatedly tested all the wires back to the ignition switch.
 
It has run many times now but keeps loosing spark and now it would appear the timing, nothing else has changed that I am aware of there in lie the mystery. Thanks  

Thesmallenginehobby guy I can get those pictures for you but not so sure what they will tell you or why the throttle has anything to do with timing and spark issues. "If you think it's electrical it's gas -- if you think it's gas it's and electrical issue" I get it, give me a few days to get the pics. I appreciate the help here guys -- I really don't know what to do, never had this problem before usually I can fix anything but this has me stumped.
 

The valve clearance check is done on a cold engine.  
 
The breather cover on the rear of the engine hides where you want to be.
Carb linkage and the intake manifold should allow access to it.
 
Also, have you tried running the engine with the kill wire disconnected at the coil?
 
As for the the throttle cable pic request, as you noted, have nothing to do with your issue.  ????
 
 
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Just curious but how are you checking for spark? Tried another spark plug? Spark plug fouling out?

I know how it sounds because i felt the same way... I had a problem with a 99cc Honda and i got soo frustrated with it I took it to a professional multiple times and he couldn't seem to fix it.. after much money WASTED an older guy that used to work on small engines told me how to fix it and its been running great ever since! I would tell you what to do but I'm afraid it might confuse you if the throttle is not made the same. The problem is than your engine is a little bit worn out causing it to not burn all the gas and causing many problems. All you need is simple adjustment. P.S. IF that's how the throttle is made.