Yes, I already mentioned that above.
I bought a new 30 pin connector cable and tried it on the second day of my trying to get this fixed. It gave the same results as the first cable did.
I might try removing all the apps off it first (except for ones that have important stuff I don't want to lose), then back it up again and try to restore it.
I have also read about putting the iPod in recovery mode and then trying to restore. I will need to read up more on that method.