I drive a similar car (99 Chrysler 300M) I had dimming issues until I changed out my alternator to a High output one. I also use an Optima Red Top as my up front battery. I would suggest going with the red top and I would redo the big 3 with 1/0 wire. For what you're running it may be overkill, but it should fix your issue. It fixed mine and I am running over far more power than you are. As some have already stated, the cap is not going to help your problem. It was just something they sold you to get over. You could have put that money on your battery or bigger wire.
Take back the battery if you can.
Take back the amp if you can.
Buy some bigger wire from Knukonceptz.com to redo your big 3 with
Come up with a budget and a goal for your system
sell the cap to some dude on Craigslist.
Sometimes rushing into things is not always the best way. You'll get a lot of shit on here for some of the questions and decisions you ask and make, but stick with it. This is a fun hobby when done right.