Before you get carried away, I'm going to suggest three things:
1) Uninstall AVG.
You can only have one real-time antivirus installed, and Avast is the one of the two that you should keep.
Use the AVG Remover from the AVG site to *completely* remove AVG.
> AVG Remover: http://www.avg.com/us-en/utilities
2) Download and update the free versions of Superantispyware (SAS) and Malwarebytes Anti-Malware (MBAM), and run a full system scan with SAS and a *quick* scan with MBAM; and let them remove what they find.
> Superantispyware: http://www.superantispyware.com
> Malwarebytes Anti-Malware: http://www.malwarebytes.org/products/malwarebytes_free
3) You should now be able to install Avast.
If not, then use Avast's Uninstaller from their home site to uninstall it, then reinstall it.
> Avast Uninstall Utility: http://www.avast.com/uninstall-utility
If the above fails, then go ahead and take drastic measures - reformat and reinstall WIndows.