battery voltage good. new battery. no amperage after it starts?

Can you help me with this diagnosis.

I have a LT1000 Craftsman mower. Problem:

It starts fine. However, it will stay running if I don't shut it off. Once i shut it down, it will not start again. Battery reads 12 volts as it should. However, someone told me that it is the amperage that starts the mower. So, the amperage is being drained very quickly. Is this a voltage regulator problem or what????? When I try starting it again, it sounds like the battery is just dead. It's a new battery!! Started quickly and then nothing. Email me paralegal37@yahoo.com

Thanks
Gary