HELP !!! 1997 Intrepid / car alarm and battery problem

Hello -

Here is my situation and sorry for the long post......

Around the middle of July, we used one of those cigarette lighter adaptors to fill up the kiddie pool over one weekend....silly us, left the thing connected, but not turned on for a couple of days with the door ajar. Well, 2 days later, tried to start the car and it was sluggish, but it did start. Also, have an Audiovax car alarm installed whish start acting funny and seemed to have a mind of its own. I would de-activate the alarm, it would go off on its own whenever it felt like it. Tried to start the car one day, car would not start. Got one of those battery chargers and was able to charge and start the car. Long story short, did no have a need to use the car for about a month, tried to start the car again and with the battery jumper hooked up, the interior lights would come on, but would flicker. The car would start when trying to jump it, however, you had to keep your foot on the gas and as soon as you took your foot off, the car would die again.....

Do you think a new battery would do the trick? Also, does anyone know how to remove this Audiovax car alarm? Is there a fuse that needs to be removed or do I need to take it somewhere to have the alarm taken out?

Thanks in advance !
Meg Kelley