OK - here's the test about whether some money-waste may have just occured.
Turn your car off and give it some beans, see if the lights dim. If they do, your battery is poked, get a new one.
If they don't, then what's happening is the dimming you're seeing is the drop from 14.4v (charge voltage from your alternator) to ~12.5v (loaded voltage of a normal battery). Your alternator is probably only a 90A jobbie. It takes probably 40 odd amps just to run your car so there's 50A for other stuff. So as soon as your audio pulls >50A (which happens quite quickly really) your voltage will drop from 14.4 to 12.5.
A cap will help slightly but the only true solution is a high-output alternator which costs $$$ out here and who knows if anyone makes one for a subey.