Your MBAM log says "No action taken".
Re-run MBAM, fix all issues and post new log.
Then try Revo to uninstall AVG...

Revo Uninstaller is more thorough in deleting programs on your computer than using the Add/Remove option in Windows. Since it is a more powerful tool, please be sure to follow the instructions carefully.

Please note there is a chance when you look for this program to uninstall through Revo it might not be listed because of the previous uninstall. If that is the case simply stop and let me know.
  • Please download and install Revo Uninstaller Free
  • Double click Revo Uninstaller to run it.
  • From the list of programs double click on the program you want to remove
  • When prompted if you want to uninstall click Yes.
  • Be sure the Moderate option is selected then click Next.
  • The program will run, If prompted again click Yes
  • When the built-in uninstaller is finished click on Next
  • Once the program has searched for leftovers click Next.
  • Check the items in bold only on the list then click Delete. You may have to expand some folders by clicking the "+" mark.
  • When prompted click on Yes and then on Next.
  • Put a check on any folders that are found and select Delete
  • When prompted select Yes then Next
  • Once done click Finish.