I searched and searched but did not find a previous post with a problem like mine.

My 98 1.8T is doing some weird things, which are causing my battery to drain in a matter of a couple hours. The buttons for the power windows remain illuminated after every otherlight in the car has gone off, except for a faint battery light in the dash.
The alarm no longer beeps and activates at the second turn of the key, but instead does it after a third turn and unlocks the doors again. The also doors do not respond to the keychain.
I am thinking the battery made need replacing, but I am worried there are much deeper problems that may continue to drain a new battery.