1992 Ford Lincoln Mercury - Grand Marquis

Well kept-up car with no modifications or after-market accessories except new radio put in 5 months ago.

Car started fine one morning, drove 3 miles, stopped at store for 5 minutes, when returned car wouldn't start. Turned on headlights and had someone watch as I cranked it over. Headlights didn't diminish at all, interior lights dimmed as engine tried to crank.

Battery was a couple of years old, so put in new battery and was able to get back home. Tried running car in park and used a simple voltage meter to check battery status, and the battery drained and car stopped in about 2 minutes.

Put battery on charge while pulled off alternator to have it checked at Autozone. It checked out fine, but decided to buy a new one anyway. Put in new alternator and battery still drains within a couple of minutes.

Is there a common fix for this type of situation or any obvious plays to start looking or standard procedures to tracing problem?

Thanks,

Chris