Battery drain

Hi all
Posting this for my Dad who has a 1995 Buick Skylark.
The problem he is experiencing is a dead battery after the car sits for about a week. The battery was about 11 yrs. old, so he replaced it. Not the problem. No lights are staying on. Dome, trunk, etc.
Thought I would try here first in case there is a common problem with this model some one knows of.
I plan to scan it for codes, but I doubt if that will show anything.
Other than the battery drain, the car runs, drives fine.
Any ideas?
Thanks, Randy

Thanks for the reply. That sounds like a very easy way to track down the problem.
Randy