When people got the "No disk in drive" error in the past with other versions of Spybot,I believe it mainly happened when people were doing a Spybot scan.Looks like your "No disk in Drive" message is popping up from the sdtray.exe,so I assume it's a different issue.
Have you been getting the "No disk in drive" error after installation,or did it only happen during the installation?
When installing,did you install Spybot to your C drive?