Is this an aftermarket alarm system? I had an aftermarket system in a Jag that started sucking the battery dry when parked because of a faulty brain. Ripped that sucker out and the problem went away.
I would have led you to the OVP relay, but since you can get the car to start by switching the A/C off or unlocking the car, it seems like the fault is the "non-factory" component, namely, the alarm.
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car