Ipod touch won't stay on

First, there are possibility that your iPod just out of battery, not enough to boot.

You might want to turn on and immediately connects to computer or if possible, to the direct charger.

If it turned on, wait for while and then go iTune and restore.

If not, you can at least locate the local apple store and let them take look at it.

They might ask $ for repair but it shouldn't be so expensive.

you might try resetting your iPod (hold down SELECT+MENU for a few seconds) or restoring your iPod back to factory settings in iTunes just to make sure that it's not some type of software glitch?

hope this helps