That's probably a 4th gen iPod, and when you do a Restore using a USB connection, it will ask you to connect it to the square white power adapter that came with those iPod models, as the last step of the Restore process. Third-party USB power adapters often do not work for this purpose (some do).
NOTE: Those 4th gen iPods also work with a FireWire connection, and when you do a Restore over FireWire, it does not ask to be connected to the power adapter. Later iPods that only work with USB do not have this requirement to connect to a power adapter during a Restore.
You'll probably need to get an Apple power adapter, or find someone who has one. If you have an Apple Store that is conveniently located, maybe you can make a reservation at the Genius Bar and ask them to connect it to an Apple power adapter for that last step (do NOT have them to the complete Restore on a Mac, if you are going to be using the iPod on a Windows PC).