Small Engines (Lawn Mowers, etc.): Engine backfires, carbon buildup, carburator

Question
I have a three year old Craftsman rider with a 26hp B&S engine.  It recently started to lose power when the deck was engaged and eventually died.  I was able to start it after awhile and it now backfires a lot.  I cleaned the deck, and changed the plugs.  It starts easy now but it backfires when I engage the deck and when I shut it off.  It still does not have full power with the deck engaged.  What should I look at next?  It appears to backfire through the carburator. The plugs also had a high carbon buildup.

Answer
Sorry it took so long,the All Experts server has been down.

Have checked the fuel filter or air filter?  Usually, backfiring is caused by a lean carburetor, but the plugs generally doesn't have high carbon build up.

The problem is probably in the carburetor.  Your carburetor is a fixed jet style,no adjustment,and is very sensitive to any dirt or debris.  If the fliters are clean, then I would remove and clean the carburetor.

Did the problem start suddenly, or has the mower sat for a while over the winter?

Let me know.
Eric