If you kill a several year old battery by leaving the lights on overnight, a cell might short and the battery won't hold a charge.

Disconnect the battery, trickle charge it overnight, then remove it and take it to an autoparts store for a load test. If bad, buy a new battery. I think your size is a Group 49, which should be relatively common.

I don't think a battery booster will hurt the electrical system as long as you didn't reverse polarity.

After the new battery is installed check system voltage to make sure the alternator is okay. It should be 13.5-14.5 volts with the engine idling with accessories off.

Duke