Stereo & Electronics - Battery and alternator bad, or just battery?

So I went to look at this F-body that I am considering buying. It needs a little work, but the price is right. We had to jump it because the battery was 100% drained. My 450 amp jump starter wasn't enough to get it going, so we had to bring out another car to jump it. It started and idled fine for about 2 minutes. Then I go to open the door and the thing just dies. Would this mean that the battery is just completely shot, or that the alternator is bad as well?

It could mean that the car is a piece of junk! It could be something other than the battery or alternator. Check for codes.

Check the voltage with a Digital multi-meter