I had the same problem recently with my 95 Jetta. I replaced the battery first, then removed and bench tested the alternator. Turns out it was the a simple fix. The connector on the wire from positive battery terminal to alternator was badly corroded. Apparently the alt current wan't making it to the battery. NAPA made up a new cable for me for $7 and I installed it in a half hour. Car has been running fine for 6 months now.