That is probably a 4th gen iPod U2 special edition. For the 4th gen iPod, if you are using USB (not FireWire) to connect it to the computer, as the last step of the Restore process, you need to connect it to an Apple USB power adapter. It has something to do with voltage, and the USB port on the computer does not provide it.
NOTE: If your computer is a Mac, and it has a FireWire port (and you have a FireWire docking cable), when you do the Restore over FireWire, there is no step to connect it to an Apple power adapter. FireWire apparently provides the right voltage.
I have the original adapter but no cable
Is that because that original power adapter is for use with a FireWire cable? I don't understand the part about "a curved USB-type cable for the adapter."
If you are using USB, you need to connect it to an Apple USB power adapter. If you don't want to get one, and there is an Apple Store nearby, maybe you can take your iPod there, and connect it to one of their power adapters to get passed that step in the Restore.