First, do you see the battery indicator icon change to the plug icon 1/20th of the time? Or does it always change to the plug and just Activesync doesn't work?
Meanwhile try this and report back (not foolproof as there are other possible paths to troubleshoot this):
1. Connect your phone to a different USB port on your computer.
- If the problem goes away, its the port on your computer
- If the problem persists
- Try a diffferent USB cable
- If the problem goes away, its the cable
- If the problem persists, go to 2
2. Connect your phone to a different computer
- If the problem goes away, its your computer
- If the problem persists, its your phone