See my previous post and here's what will probably be my final thought. Get SP3 from...
http://www.microsoft.com/download/en/details.aspx?displaylang=en&id=24
…you can ignore the text that says that it is for network installations and also ignore the text advising Windows/Microsoft Update if only updating one PC. Ignore any recommendation from Microsoft to use Windows Updates.
Then run the download to (re-)install SP3.
I am getting desperate with a customer's PC at the moment and they don't have a listing for SP3 in "Add or Remove Programs" either, neither do they have the
c:\windows$NtServicePackUninstall$ folder. The PC has nonetheless let me do a SP3 installation. This is perhaps not quite as good as uninstalling SP3 first but may just solve the problem. If you are resigned to a clean install anyway it's a free hit.
It didn't solve my customer's problem (though it hasn't seemed to make matters worse) but it might solve yours.
Tricky