First two problems: Dell. Vista. Get rid of at least the second one. Starting fresh is my recommendation. It's going to be the most cost and time-effective for everyone involved.

Networking problem... You didn't happen to use the same patch cable that was already in place when you connected your personal machine to that other switch did you? Other than that, try a completely different brand/model of switch with a new and preferably pre-tested patch cable - with your computer.