Craftsman tractor 917.250551 won't stay running

I have a Craftsman garden tractor (don't know the year but it is pre 2000), model 917.250551 with a 50" deck and a Kohler 22.5hp V-twin engine. I was using it recently when the engine died like it had run out of gas. I checked and still had plenty of fresh gas. The carb had also recently been cleaned, along with new fuel and air filters and the battery was new. When I went to restart, the engine would not turn over and I found that the battery was dead (weird). I hooked up my battery charger and was able to start the engine, but it only runs for about two seconds and immediately dies again. I can easily start it again and again (as long as I jump it) but it won't stay running. Gas flow seems to be ok.
A few people have suggested the fuel pump as the possible culprit, but the brand new battery that was dead seems strange. Is there a bad alternator or regulator that might be causing the problem? I saw a reference to the regulator/alternator in both the troubleshooting section and the schematic in the manual, but don't see either of them in the parts listing in the manual or online.
Any help is appreciated. Thanks!
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