The trunk opens and the radio comes on by itself.

This sounds a lot like an Alternator problem. I would have the AC voltage output checked. AC Voltage can cause electrical demons. stevieray1: The way an Alternator works is it generates AC voltage then the diodes change that to DC voltage. An alternator with diode problems will leak AC voltage into the vehicles electrical system. This is a common misdiagnosis on a lot of electrical problems resulting in 1000's of dollars in repairs to correct Electrical problems. I would still check the AC voltage output and the overall charging health of the alternator. Anything more then 0.05v is too much. I normally see 0.5v or higher when we are running into similar issues in my shop. Also check the DC voltage for sure, that should be 13.5-14.5v anything more then that could also cause a similar problem.

IT'S NOT AC VOLTAGE.IT IS DC VOLTAGE OUTPUT!

Was ignition switch on?... Was the battery cable polarity momentarily reversed? .. **Correct** installation of a battery should not have any affect on the electrical system on that year model..! However if there was no subsequent damage...... Drive on!!!! .. Won't get into the ACDC debate... I like ACDC! .. But the alternator wasn't turning! .. I guess(?) .. Who knows??