Mac App Store thinks I don't have any apps installed
You'll want to focus on problems with either Spotlight finding the apps or perhaps an overall disk structure failure.


Spotlight: How to re-index folders or volumes - HT2409
Spotlight indexes wrong HD
Using Disk Utility to verify or repair disks - HT1782 


Unless you are going in and systematically modifying each app's receipt, the App Store should find apps using spotlight and correctly reflect the status assuming both the disk doesn't need repair and the spotlight index is current.