these cars take A TON of power to start. I think 80amps was once told to me. If you kept starting it and stopping often then you could have killed the battery. When you say ran for 20 minutes you meant driving it right? these engines don't produce much power idling, so idling does next to nothing for a dead battery. A quick test to see if you alternator is working is to measure the voltage at the battery with the car running and the engine at about 1500rpm. Should be at about 14volts. EVen if it is showing voltage the reg could be shot, but this would give you a decent idea. Try charging it overnight. If it won't hold a charge then you know your problem. I got a new battery for 55 bucks from autozone with a pro-rated warranty for 10 years. Not too shabby. Hope this helps,
Ryan

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83 300SD.......sold
96 integra SE....sold
99 a4 quattro....sold
2001 IS300.......sold
2002 330i.........current.
2004 highlander limited....current.