When you connected the Nano to your PC, did anything change on the iPod's display? Did it appear to charge at all?
I assume you have worked through each and every suggestion in this Apple support document?
iPod not recognized in 'My Computer' and in iTunes for Windows
and connecting to a friend's PC which didn't work.
If the Nano is not being recognized by two different PCs, that rules out the possibility of an issue with your own PC and points to an issue with the Nano. Check the Nano's dock connector port for any signs of damaged/bent pins or corrosion. If there is any debris lodged in there, take a can of compressed air and perhaps even a soft brush of some sort to dislodge and remove it.
Otherwise, you may need to take your iPod in for service or replacement.
B-rock