Small Engines (Lawn Mowers, etc.): Loss of power, briggs stratton engine, sears craftsman

Question
I have a Sears Craftsman Model # 917.256531,Briggs& Stratton Engine Model # 28N707, Type #0173-01
This engine starts but has no power, the only way to keep it running is at full choke,then it back fires,it seem like the timing is off.  I have taken the flywheel off check the key thats o.k.,Everything under the flywheel looks good, muffler was bad just before this happen,Air filter was dirty, What my next step? the carburetor!! What about the "After Fire Solenoid"?  Thanks AL

Answer
Al
Try these soulitions or rule them out if it doesnt pertain to your problem.

Spark plug is fouled, improperly gapped, or damaged.
Breaker points are pitted or improperly gapped, breaker arm is sluggish, or condenser is bad.
Carburetor needs adjustment or service.
Fuel line, fuel filter, or fuel tank cap vent is clogged, or fuel shutoff valve partially closed.
Valves not adjusted properly or valve springs weak.