Audio Systems: Is it a damaged capacitor causing the problem?, gel cell battery, amp fuse

Question
I have:
Gel cell battery
1.5 farad capacitor
2 amps (1000w, 400w)
DVD
Kenwood Excelon 990

I recently left my stereo system on all night. The next day the system was still "on" but quiet. Car wouldn't turn over at all. I left everything connected and simply attached my battery charger to the terminal connectors. I did not properly power up the capacitor using a resistor. It all seemed to be adequately okay for several days after that.

Then I started to get a loss of sound when I turned my volume up too high. For three days of heavy use it seemed to get worse. I could not turn the volume past 1/2 way without the loss of sound. This problem occurred once before with the same, but earlier model receiver I had when I hooked it up on a boat without enough juice going to the constant power to the receiver. So I increased the wire size to the receiver. No luck. So I grounded the dash components better (they seemed to really need it). The problem persisted. Today I noticed that my headlights were dimming during peaks and the sound quality was deteriorating. Similar to when the capacitor is absent. I'm wondering if the capacitor is damaged. Or maybe my battery (which reads 13-14 volts) lost it's amperage. The reason I focused on the dash components is because the DVD player seemed to suffer starved power as well when it paused at high volumes, and the FM tuner was less affected by the problem when I turned it up. Worth noting is the 50 amp fuse between the battery and capacitor that I purchased without knowing the proper amp rating I should use. I would just buy another capacitor, but I am poor at the moment. I pray that the stereo is not damaged because I know that the Kenwood authorized repair shops charge way to much. Any inexpensive trouble shooting suggestions?  

Answer
I would say you need a new car battery.  once a battery is fully drained it never comes back to 100% especially if it's got 18 months or more of use on it.
I'd be very suprised if your cap was bad.  the only reason you need the charging resistor is to cushion the difference between the uncharged (0 volt) capacitor and a fully charged (12.5 volt) car battery.  if battery goes dead the capacitor goes dead with it so there is no voltage difference and putting a charger on the battery will only cause the battery and capacitor to charge slowly over time just like the resitor would do, so that wont hurt the capacitor at all.  
There are several places you can take your battery to have it tested free.  (autozone to name one) batteries contain many cells and if one of them becomes weaker than the rest it will perform very porly under load but usually will show good voltage with no load.  this sounds like what's happened to yours.

Good luck and let me know.