Two suggestions: run the 10.6.8 combo update (that should overwrite the existing App Store installation), or do a clean install on an external hard drive, download the Mavericks installer from the App Store while booted from that, then copy the “Install OS X Mavericks” application from the Applications folder to your internal hard drive before it installs (I did this with a supported Mac to grab the installer to hack onto an unsupported MacPro 1,1). Of course, the latter option takes as long as reinstalling the OS and requires an external hard drive, so you might as well just spend the hour and a bit and reinstall the OS...it’s not difficult, and it leaves all your installed software intact (and if that doesn’t solve the problem you can be pretty sure it’s misconfigured third party software, such as Little Snitch).
While I’m not a fan of the App Store and would prefer the option of a direct download, it works well for the vast majority of users, and it does a better job of keeping them up to date than the previous Software Update mechanism. It’s a pest in corner cases, though.