What's your Operating System?
If it's Vista, then:
Right-click on icon, select Properties, go to tab "Compatibility" and tick "Run this program as administrator". Try running spybot. If it doesn't work, then try right-click > "Run as Administrator". If fails, then un-tick "Run this program as administrator" and then try right-click > "Run as Administrator".
If it's XP, then: Right-click on icon, select Run As..., select "The following user", enter administrator's account name and password. Click run.
Edit: Do you have any found malware which Spybot found while scanning?