You can sell that shit on eebay for more than $20 so call it a steal.
Anyway...

1. Take it into apple, see if they can fix it with its warranty.
2. Let it run out of battery 100%, then wait another two days. Sometimes when an ipod is COMPLETELY out of juice, it resets some settings.
3. Google "ipod touch 1611" and see what comes up.

I've bricked and unbricked like 3 ipod touches, 2nd and 3rd gen ones, and fixed them all, it's just the right combo of restoring and rebooting.

Install the latest softa?

Or, delete everything from it (plug it on comp and delete everything), then copy from another iPod the files.

What generation?

This happened to my ipod touch last week, and i fixed it by connecting it to itunes on another computer, becuase it couldnt find it on my own one, i dunno why, but it worked. Connect it to a different computer with itunes and restore it from there, should work