Car stutters at low rpm. randomly dies at idle

[TheBlueNinja89]

ok I have a 96 rs with the 420a automatic. all stock besides bolt-ons, intake, and exhaust.
The battery went bad in it almost two years ago. I bought a battery and put it in but when it went bad after 2 months I decided I needed a stronger battery (I have a 2000 watt amp). I put a marine battery with like 1200 ca in it. fired up within half a second of turning the key and sounded amazing. the next day i checked fluids and such and the engine was running. When I shut the hood I let it drop and when it did it shorted out on the hood and the engine shut off, I failed to realize how close the positive terminal was to the hood. far as i know the only thing damaged by this was my 300 dollar stereo since then it never started as quickly or ran so smoothly but was starting and running like normal again. now my car has trouble starting sometimes and when I slow to a stop it wants to die and on occasion does die even sitting park (like 5 times in the last few months) other than that drivability is normal. could my fuel pump be losing pressure or is my ecu crapping out on me? I will test the fuel pressure soon and the compression. any input would help

 

[VelocitàPaola]

What's your battery voltage when all of this is happening? I wouldn't be surprised if your new battery was damaged after being discharged by a short. By the way, a marine/deep cycle battery battery usually has a smaller peak current rating than a standard battery of the same size. It really doesn't have any place in a car unless you run your stereo on the battery alone for a long time.

 

[TheBlueNinja89]

From the digital reading on my capacitor it's right about 14 volts when running and stays between 12.7 to 13.1 when I turn the car off. The engine always turns over easily it even sat for almost 4 weeks and started easily. But once it starts sometimes it stutters like it wants to die for a few seconds

I forgot to mention that the control module in the engine bay makes a high pitch whine after i turn the car off for about 3-5 minutes. is this normal?