Once the Device is asking to be Restored with iTunes... it is too late to save anything...
See Here > http://support.apple.com/kb/HT1808
You may need to try this More than Once... Be sure to Follow ALL the Steps...
After you have Recovered your Device...
Re-Sync your Content or Restore from the most recent Backup...
Restore from Backup > http://support.apple.com/kb/ht1766