Welcome to the discussions,
is your new computer authorized in the Store menu in iTunes?
http://support.apple.com/kb/HT1420
Any restrictions set on the ipod for app-installation in Settings/General/Restrictions?
To transfer your data to a new computer, back up manually by right clicking on your ipod in the device list and choosing "backup". Transfer your purchases the same way, set up at least one contact and event on the new computer, to be able to merge data after your ipod got erased during the first sync. Use the manual backup to restore from and all data and settings should be back again.
More info here:
http://support.apple.com/kb/HT4137 and here
http://support.apple.com/kb/HT1766