That car should have a 130A factory alternator, so you're good there as long as the alternator isn't bad. Thanks for mentioning the cap, too. Disconnect it from the circuit before doing anything else. You don't have to completely remove it, just lift the ground. You can leave the positive connection in tact, just make sure it is tight and that the ring terminals are in good shape.
If that corrects the problem, toss the cap. If not, have the battery tested and then the alternator, if the battery checks out okay.
But before all of that... go over ALL of your power and ground connections and check both the termination points and the ring terminals and make sure they're tight and free of corrosion. Also, make sure your battery posts are clean AND, make sure the factory battery ground is good. Your wiring can be the best in the world and if that ground is effed... your whole system is.
EDIT: Oh and, if you plan to use a cap, it's best to have it as close to the amp as possible and to have it grounded at the same point as the amp... again, as close as possible.