can't keep my car running

i have a 97 volkswagen golf trek. i have the 2.0 for an engine and i think that i have an elctrical problem.  my car has been running fine for about a month and all of the sudden my car died yesterday.  the battery completely dided. i got it jumped and started, but it died 5 min later.  you can see all the lights starting to dim.  so i changed the battery and it ran fine for about 20 min.  then the lights started to fade and it died again.  this morning i went out and the car started right up like it was no problem and then died again 15 min later.  does anyone have any idea why this is happening?

Prolly loose Alternator wire, any auto shop, or like Auto Zoneor pany parts place can do a test on your alternator and the battery.  Jeez I think even Wal-mart does it.