Hello progress and welcome to the forum.
Avast cannot block the Internet unless the actual site is malicious and the web shield is warning you from entering a site. The most likely cause is your firewall (FW) blocking you or a previous antivirus (AV) on your system.
First I need to know the following:
1. What is your OS, 32 or 64-bit?
2. What version of Avast did you install? 5.0.677 or something else?
3. What other security software do you currently
have or did you have in the past
on this machine including antivirus (AV), firewall (FW), and other security programs? If they were in the past, how did you remove them (the vendor's uninstaller's tool or another way)?
Check to see that your FW is not blocking any components of Avast, and report back to us with your reply to the questions above. Thank you.