Disconnect all devices from the computer except for the keyboard and mouse. Re-boot computer. Open Itunes. Connect Ipod. Should install the driver, then pop up in itunes. Do a hard restore on the Ipod before connecting it to the computer.
By your words "its broken around the home button". Being second hand, I doubt anyone will fix it. You can attempt it yourself as I have in the past. If its stuck in setup mode, sounds like it took a beating.