ok thats a tricky one.
i would be tempted to take a screenshot of my extensions page in firefox so i could reinstall them all, and then do a fresh install of firefox,
first back up your saved passwords
and i would back up my bookmarks
i use xmarks for doing this as i can sync bookmarks between computers, one saved on the laptop shows on the desktop when i open firefox again.
Xmarks | Bookmark Sync and Search
also before you do this could you check that the avg stuff is not in your control panel /programs and features,
also what anti virus do you use?