Battery drain while parked

I was borrowing my Dad's car, I think it is a 1990 or 91. It was fine for a month or so, but then one day I get in it at work and it wouldn't start. Got a jump, got it home, tried starting it again once I got here and it started fine. Figured I must have left something on. The next day it wouldn't start again. If I let it sit for (depending on the current charge of the battery) about a half hour or so, it wouldn't start again. So I started disconnecting the battery cables when I parked it. Changed the alternator, I guess the newer ones have the voltage regulator built in. Started up without a jump and still started 6 hours later. Thought it was fixed. After 12 hours of sitting, the battery was drained enough that it wouldn't start. So I guess it wasn't the alternator, but why did it improve when it was changed? I don't see anything staying on, and therefore draining the battery. I am thoroughly confused...

It probabally was the alternator, but a bad alt. will slowly kill the battery as well.

Check the alternator output, measure the terminal voltage at the battery with the car running. It should be 13.80Vdc to 14.20Vdc with the accessories off. If that checks out, disconnect the NEGATIVE battery cable with the key off and check for a spark as you gently touch it to the battery post. There may be a VERY FAINT spark, bot anything that audible or very noticeable indiactes a draw, now you've got to find it.

If all these test pass, it's likely the battery is now bad and will need to be replaced.