Version of iTunes, version of Mac OS? Has it worked before?
maybe the Itunes needs to be updated. I remember this happened with my ipod when i tryed to sync it. it wouldn't appear and if it did, it disappeared within seconds. After updating Itunes, it began syncing. Or, if you take it to the Apple store, they can fix it for you.
here is a page from the apple website that cna help u with ur situation.
link
if that doesn't work, try restoring on a different computer. It might just be that USB ports conking out because you have an old laptop.