Reddit mentions of Briggs & Stratton 794572 Carburetor Replaces 793224 791888 792358 792171

Dump the oil and put in fresh oil. Install a fuel shut off or start using the one that's already on it, Some have them some don't. Look for it, it would be right under the fuel tank in the fuel line. Rebuild the carb or just take it apart and clean it. If you're careful you can do it without needing new gaskets or the rebuild kit. Or you could buy a new one http://www.amazon.com/Briggs-Stratton-794572-Carburetor-Replaces/dp/B005F6QJIQ/ref=sr_1_5/184-7640043-4345928?s=lawn-garden&ie=UTF8&qid=1413316706&sr=1-5&keywords=20+hp+briggs+and+stratton+carburetor

Search around you may be able to get one cheaper.

A rebuild kit is about $25 bucks but it takes a little knowlage to do it properly. If you've never done it before you might be better off with a new one. And put some Seafoam in the fuel. It'll prevent gunk build up and extend the life of the new carb and maybe even prevent this from happening again.

If there is a shut off you could just turn it on when you want to use it and shut it off after. The seafoam might even free up the stuck needle valve given some time to work. I'd try this first because I'm lazy and cheap.

You should be using the fuel shutoff anyway. This is the reason that put one on it in the first place.