The above solution was only if you have zonealarm firewall installed and then had a complete loss of internet connection after the KB951748 windows update. Even if you don't have zonealarm you should still be having the KB951748 update because it is a critical security update.
At the top of your Control Panel > Add/Remove Programs there is a checkbox for
Show Updates. If that checkbox is checked and you still can't find KB951748 in the updates list then download and install
KB951748.
If you have zonealarm installed and you have the KB951748 windows update already installed, then your internet connection problem is because of ZA conflicting with the windows update. In that case get the latest
zonealarm v7.0.483.000 which works with update KB951748.
If you don't have zonealarm and you also don't have KB951748 update then maybe installing only the windows update will solve your problem.
If it doesn't, then from what you said about viruses, that is probably the reason for your loss of internet connection. In that case I recommend you uninstall Avast, download and install
Kaspersky Antivirus v7.0.1.325 > activate the trial > update it > scan and clean. If Kaspersky cleans out all the viruses then you can continue using it till the trial ends and then switch back to Avast or buy Kaspersky Antivirus.
If you still have virus problems, then maybe post a
HijackThis log in a new thread.
Edit: I mean my above post.