There are 2 other programs that are supposed to clean up what avastclear doesn’t.
http://rejzor.wordpress.com/avast-cleanup-tool/
and another one called Revo uninstaller, sorry no link but it’s at cnet.
I tried them both with no result I still have 104 avast folders I can’t get rid of. Like you I cannot get online, although my symptons are different. I’m hoping for an explanation but according to IT at Microsoft my hard drive needs to be reformatted and everything re-installed (he said without a hint of emotion).