ipod classic is not listed under source list in iTune after restore
Apple's Knowledgebase suggests a multi-step process for troubleshooting this issue. 


  
  Try the iPod troubleshooting assistant: If you have not already done so, try the steps in the iPod Troubleshooting Assistant
  (choose your iPod model from the list).
  
  
  If the issue remains after following your iPod's troubleshooting
  assistant, follow the steps below to continue troubleshooting your
  issue.
  
  
  Restart the iPod Service
  Restart the Apple Mobile Device Service
  Empty your Temp directory and restart
  Verify that the Apple Mobile Device USB Driver is installed
  Change your iPod's drive letter
  Remove and reinstall iTunes
  Disable conflicting System Services and Startup Items
  


Apple's iPod: Appears in Windows but not in iTunes contains more details about these steps.