First thing I'd check is the volt meter, and if you don't have one I'd get one! You need to know what the voltage is when the engine is running. It sounds like you may have alternator/regulator issues, and it may be overcharging and taking out electronic components.
Once you've got a meter or gauge on it, start the engine and see if voltage is over 14 volts. Ideally it will be 13-14 v. and if it's higher you've got either a bad regulator, or alternator.
Rarely will a battery cause a high voltage problem. It's almost always the charging circuit components.