If you have iTunes, then you have the songs backed up on your PC. Of course, you do this at your own risk.
From this page:
"If that method doesn't solve your problem, you may have to restore your iPod touch. To do this, hold the Sleep/Wake and Home buttons down for at least 10 seconds, until the iPod touch shuts off and begins to restart. You can release the buttons once you see the Apple logo appear."
"If neither of those works, the next place to start is resetting all of the settings on your device. Go to Settings -> General -> Reset. There will be a few options, but try Reset All Settings first."
The page has a few other things to try.