I had the same issue. I have just updated to Avast 2014 and my IE 10 stopped working. I have first updated IE to IE11. That didn't help. Than I disabled the avast plugin, reset IE setting, that didn't help either. I went to Control Panel, Programs and Features and modified avast to remove browser protection. That also didn't help.
I have uninstalled avast 2014, rebooted, than installed it again through custom and unchecked browser protection. Now I have avast and IE both working, so I recommend that people try this...
I have found a setting in Avast (Settings/Active Protection), Web Shield, perhaps setting it to off would help as well?
I would really like if avast did admit there was a problem, like that I would install the browser protection when the problem is resolved, otherwise, I will have to go through all this periodically to find out if the issue is resolved because I like to have an antivirus plugin...
Alternatively, it would be great if plugins for different browsers had different config option, so I can enable Chrome one for example...