Place the iPod in recovery mode using one of these programs and then restore via iTunes:
For PC
RecBoot: Easy Way to Put iPhone into Recovery Mode
or
http://joshuabailey1997.wordpress.com/2010/09/02/recboot-v1-3/
If necessary:
Download QTMLClient.dll & iTunesMobileDevice.dll for RecBoot
and
RecBoot tip
RecBoot may have problems on 64X windows, then try:
Tenorshare ReiBoot – Enter & Exit iPhone, iPad, iPod Recovery Mode with a Single Click
For MAC or PC
The Firmware Umbrella - TinyUmbrella
Installs blootware on PC too
For how to restore:
iTunes: Restoring iOS software
To restore from backup see:
iOS: Back up and restore your iOS device with iCloud or iTunes
If you restore from iCloud backup the apps will be automatically downloaded. If you restore from iTunes backup the apps and music have to be in the iTunes library since synced media like apps and music are not included in the backup of the iOS device that iTunes makes.
You can redownload most iTunes purchases by:
Downloading past purchases from the App Store, iBookstore, and iTunes Store