If you hve not already, shut down (power off) you computer. If other USB devices are connected, you may want to disconnect them, except for standard USB keyboard and mouse (if normally used). Do this to Reset the iPod
Turn on computer. Run iTunes. Connect iPod to a direct USB port. If the earlier Reset did not turn the iPod on, try it again while it is connected to power from the computer
If that does not help, I think you ruled out a bad USB port, but it could be a bad USB cable. If possible, try the iPod with another USB cable, or try the cable you have with another device, to rule out bad USB cable as the cause.