seeking list knowledge - auto electrical

[Livolsi, Stephane]

I'm helping a friend troubleshoot an electrical problem in his (non-Audi)
car - it's a plymouth laser - NAC but it is a turbo ;)

Anyway, he just put in a new battery3 weeks ago, and about a week ago he
started getting slow cranking at all times, and occasionally would not even
start, even after just being shut down from a short drive.

I put the DMM on the car and found this.

Voltage at the battery (car off) is about 10.5
Voltage at the battery (car running) is a steady 14.3
Shut the car off and voltage drops right to 12.5 and then starts dropping at
about 1 volt every 2 secs til it gets to about 10.5
Shut the car off, disconnect the battery and voltage shows steady 12.5

Assumptions:
Charging system is good
Battery is good
There is a short somewhere that is causing a current drain.

The car does have some fancy dancy alarm system that may or may not be
working properly as well as a very involved stereo system (2 amps,
isolators, etc).  I think the alarm system is a likely suspect.  My friend
bought the car with it already installed and doesn't know anything about how
it's wired.

With the car off and key out there is about a steady .14 amp current draw.
Does this seem high?

Stephane