Dead battery, I think i have a big problem?

Ok, so here's the deal. I put my car away for winter storage, and being an idiot, forgot to disconnect my battery. Connected to that battery, I have two 900 watt mono amps and in turn, a 5 farad cap. My battery is now stone dead, and the car will not stay running once the booster cables are removed. Now i realize this is because the cap is pulling any charge it can, trying to recharge. I obviously have to disconnect the cap to get the car going, but could my alternator have been affected? Or just the battery? And secondly, how do you charge a cap? My installer did it for me the first time and didn't think to tell me how, I need help, thanks.