As I said in previous reply, IF the hard drive is faulty, you won't be able to do anything to recover data from the iPod. Based on your description, it sounds like the hard drive is faulty. The iPod keeps resetting itself, because the bad hard drive prevents the iPod from starting up properly, and it's not going into Disk Mode for the same reason. And if the iPod cannot start up (either normally or in Disk Mode), there's nothing there for iTunes to see when you connect it.
It won't help with getting your data back, but if you want to keep using the iPod, there are options for replacing the bad hard drive. I mentioned one option in previous reply. There are others. My "classic" iPods are much older (with black&white screen), but I replaced their failing hard drives with Compact Flash or SD cards (on difference adapters). And with new batteries too, they work better now than when they were new, including higher storage capacity.
Going forward, you should keep all of your songs in the computer's iTunes library, and back up that library in case your computer (or its drive) fails. This Apple document describes one way to do it, using an external drive for the backup.
Manage and back up your iTunes media library - Apple Support