Small Engines (Lawn Mowers, etc.): Tecumseh wont run right, carbureator, throttle lever


Question
I have a WeedEater 42 inch riding mower, purchased around
2000.  It was used very little for a year then stored since
then until I started using it again this spring.
The info on the Tecumseh engine is as follows
Engine Model  OHV 17    204601A  (C)
Engine family  STP490UIG2RA
Displacement  490   D.O.M. 7077S
It ran ok but every once in a while it would pop  or back fire out of the exhaust after I shut it off.
Now it won't run unless it is partially choked off and then
only for ten minutes or so.  I took the carb off to clean it and made sure the filter was clean and gas was getting to
the carb ok.  Put it back together and it does the same thing.  It will pop out the exhaust when I can get it to run and sometimes it sounds like it is popping back through the carbureator.  In the slot where the throttle control slides there is a notch that
when the throttle lever was in, it used to run good. Now I have to push the throttle control up towards choke above the
notch an 1/8 or a 1/4 of an inch to get it to run. It will run there until it gets warmed up good then it dies and won't start again until it cools down.  I am very mechanical, I have straighted bent cranks on push mowers, installed carb kits on older normally asperated vehicles, and overhauled V8s but I can't figure this one out.  Thanks in advance.

Answer
First off, does this model carb have a electrical fuel solenoid on the carb bowl? This shuts down fuel when the key is turned off and allows fuel when the key is turned on. Make sure it is doing such if it has one. If not after making sure you have a good fuel supply to the carb, your needing a carb rebuild, the engine is starving for fuel. Once you go beyond the high idle notch on the control you going into a choke position, so that your making up for the fuel it can't pull on it's own and now limiting the air flow to make it run richer (more fuel). By tweaking the choke plate to a more closed position you kind of adjusting the carb to compensate what it's not getting on it's own. As long as you have a good fuel supply to the carb, you need a rebuild..........Tom
And thats my fault? So you kill my ratings because your mad at the site? The information I gave you was good. It's not my fault we get maxed out and your having a problem with a follow up question. Do you expect us to sit here all day and just answer questions non-stop? Out of the goodness of each of our hearts we try to help people out, let's understand one thing right off the bat, most of us get paid good money during the day for the free advice we pass on to you free! The only thing in return we get is ratings. It's people like you that are ungrateful, and make us wonder why we even do it . The answer is simple, for the NICE people that do appreciate it. If your such a mechanical whiz fix it yourself. It's a simple fix. Especial for such a gifted repairman of aspirated vehicles as yourself..........Tom