DC Battery Problem

Hello I have had a 94 Dodge Caravan for about 10 years now and I have been running a few things like a laptop w/gps software for years out of the lighter socket with no problems. About a year ago I purchased a 94 Plymouth Voyager which is essentially the same vehicle with the same engine and alternator etc..
The problem is that on the Voyager when I reconnect the battery it causes the laptop or anything else I have plugged in to turn on by itself and also the battery gets drained frequently.
If anyone has any ideas on this please send them my way, thanks!