Thanks.

I just tried uninstalling Browser Protection and reinstalling it, but that didn’t help.

I noticed that IE uses the 64-bit avast! plug-in for both the 32-bit and 64-bit versions of IE 11, which seems odd since the avast directory has both 32-bit and 64-bit versions available.

I noticed that you, too, are running Windows 7 x64-bit (SP1).
Is your Windows 7 Home Premium?
Do you have both 32-bit and 64-bit versions of IE 11 installed?