Most likely, the problem is your USB cable: these appear to be very delicate. Try a different cable (you can get new ones for about $1 on ebay).
If that doesn't help, then it's most likely the drivers on the PC. This is a total PITA. You need to:
- uninstall the drivers (I think there are two things here but it's a while since I had an HTC)
- uninstall the HTC Sync software
- restart the PC
- restart the phone
- reinstall the HTC Sync software
NB: do NOT connect the phone until prompted then be sure to allow ALL the drivers to install before disconnecting - probably safest to walk away and leave it to do it's thing for a good 10 or 15 minutes.