Does anyone know the file name and path for the file containing myibay bid information (eBay auction id, my maximum bid etc.)? I didn't see this info in the FAQ section and was unsuccessful finding it by searching the forums.

My hard drive is about to die and I'd like to make a copy before it does.

All information stored on the remote server.
So once you login using the same eBay user id on another PC, then all your snipes will be there.
There is no need for a backup in this case.