2000 Volkswagen Jetta Idle Problem

2000 Volkswagen Jetta 4 cyl 90000 miles

I just recently replaced the battery on my Jetta due to cold weather killing the old one. Ever since I put the new battery on (about 3 weeks now), my car has not been running right. When I'm not moving either in neutral or with the clutch in, my idle is just fine right where it's supposed to be. But in the car is in motion (say, I'm stopping) with the clutch in or in neutral, my idle will drop to just barely above 600. The engine starts sputtering and I can watch my headlights dim, etc. Did I maybe mess something up when I changed the battery, or is there a bigger problem? (And I've already added more than 100 miles since I changed it, so the "drive until the computer resets" trick doesn't work)