The deep-cycle batteries can take a few total discharges and maintain voltage potential under load, but not the standard lead-acid.
I wouldn't try reviving it from the dead unless its pretty new(batterys don't last more than 5 years anyways), it will probably be sufated beyond redemption, and then I'd trickle-charge it in a safe area and cross the fingers.
By the way, don't fast charge a battery in a rental unit, it may boil over and put a hole through the carpet
. (I'm trying to make every mistake possible-at least once.)
You can check if there's a key-off short by putting an ampmeter across the disconnected negative battery terminal. Over half an amp and above(clock, radio, alarm,,CPU) tend to indicate a problem. Pull fuses untill it stops.