I'm going to guess that the lightning audio amp kit you bought that's rated at 350watts is probably a 8ga kit. It would be nice to have had a 4ga kit instead, but I don't think that the wire is the problem. A 1/2 farad cap might help the probelm, but I doubt it would solve it. I would guess that it is the weak alternator. You can get your stock alternator rewound at some places for about $200, and it will be able to put out more current.