00 Vr6, alternator??

[New2GasEfficiency]

for the past two weeks ive been having a little trouble with my car.. i only say little because for the moment i have been driving my dads truck because he is in recovery for surgery... otherwise this would be a huge problem. I have exactly a week to find out what the problem is otherwise i have no ride to school or work.... 2000 jetta Vr6 5spd 105,000 miles. about three weeks ago my epc light came on, it had done that before and then turned off after a day or two.. well this time it didnt go away. 2 days pass, my car idles at about 1000 instead of the normal 850(giveortake) one day it hesitated to start, didnt seem to have a strong crank but it did fire up and no problem. once i get to my destination i turn the car off about 1 hour later i get back in and i get nothing, not even a bump from the crank, i popped the hood and noticed neg. post had some corrosion built up, cleaned it off got a jump, fired with no problem, got home turned it off and immeadiately tried to crank it up again. Nothing.. changed neg. cable out,(had to use a universal cable and the chasis ground is a 12 gauge, much smaller than the previous 2 gauge) charged the battery for about two hours, dropped it in and the car fired up, ran for half a day and same problem arose.... local garage says battery cant hold charge due to bad cell, autozone tells me its the alternator, i cant seem to get a straight answer i have a feeling its more than just the alternator, i also have no brake lights.... some one please help????