Windows 7 Build 7601 This copy of Windows is not genuine - help please

Hmm - try right-clicking on them, and using the Run as Administrator option that should show.

Right-click on the AVG Remover executable - I suspect that it's running as a standard USer fr some reason, so doesn't have full access to the registry.
If that doesn't change the error messages, then we'll have to start messing with registry permissions - but I don't fancy attempting to track teh changes through the registry, much

It's a possibility, if there's registry corruption that has locked you out of parts of the registry.

Please navigate to the first of the registry keys shown above, and right-click on the Key - select Permissions.
What are the users listed, and what permissions do Administrators and Users have (if any).

I have seen this sort of thing cured in the past be reinstalling the program, and then uninstalling it again - but I'm reluctant to do that with AV's because they tend to set up some serious self-protection, and also becuase it's difficult getting the same version as is 'installed'.

OK - use teh RE-oorder button and see what comes up.

What a mess of potage that lot is!
Change the Administrators permissions - ONLY to Full, using the Advanced options.
then put a tick in the 'replace all child...' box, and click OK out.
repeat for the other 'stuck' keys and then try running the AVG Remover again.