App Store thinks apps are installed
Try the following steps in order:


Quit the App Store
Eject all disks (including any .dmg files you have mounted)
Use Spotlight to search your hard drive for anything with a similar name to your application.
If you find anything related to the application in question remove those files.
Delete the file at ~/Library/Preferences/com.apple.appstore.plist
Delete the file at ~/Library/Caches/com.apple.appstore/Cache.db
Delete the file at ~/Library/Cookies/com.apple.appstore.plist
Delete the file at ~/Library/Cookies/Cookies.plist
Open terminal and run this command: /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user
Logout of your computer &amp; log back in
Reopen the Mac App Store
Try to install the application again.