When uninstalling the older version, did you make use of the AVG Remover tool? If not, it can be found here:
http://www.avg.com/ww-en/utilities - Read AVG installation is failing for detailed instructions. Bypass the offer to pay a fee for remote help!
The sticky at the top of the AVG forum titled "AVG 2012 (incl. Previous Versions) Uninstall / Re-Install Instructions" should also apply to installing AVG 2013. The only exception would be at the bottom of the page, where they provide a link for the AVG 2012 offline installer. That same link should bring you to where you can find the 2013 offline installer.
Some have also had success installing AVG in Windows Safe Mode.
If you continue to experience problems, I would further suggest you post at our AVG Forum.
Best of luck..
I keep getting the error message:
Error Code 0XE001003D - installation failed.. please help! I uninstalled my old version figuring that would help but it didn't. Thanks!