IM wondering if I need to buy a new car battery.

It's five years old and near the end of its life expectancy. A good battery can only be expected to stay charged enough to start the engine for three weeks. That's because of all the computers' memory circuits drawing constant current. A five-year-old battery is doing good if it can still crank the engine after sitting for a week.

Once a battery becomes very discharged, it will take a good 15 to 20 minutes on a charger, (or driving the car), for the acid in the battery to become conductive so it will START to take a charge. At that point it will need at least an hour charging at a slow rate to become fully recharged. 12 miles isn't enough time to fully charge the battery. Then you let a discharged battery sit for another week so it can be expected to be nearly totally dead. You might be able to save it yet but charge it at a slow rate for at least an hour. Charging it at a high rate will destroy an old battery or hasten its eventual failure. The generator on your car puts out three phase current which is very steady. Home battery chargers put out rectified single phase current which turns full-on and full-off 120 times per second. That causes the plates in the battery to vibrate.

The lead flakes off the plates as the battery ages, and those flakes build up in the bottom of the case. When they get high enough, they short out that cell. When the battery charger vibrates the plates, that lead flakes off faster.