Yahoo Instant Message requires shockwave Flash object to be enabled in the Tools > Internet Options > Programs > Manage Addons. Show all addons to see if the Shockwave object is enabled. AVG may alse requie the same object.
You might need to upgrade to IE8, though., as the shockwave object version in IE7 or earlier might not be compatible with Yahoo IM or AVG.
Also, you'd need AvgFree version 8 or later.