Hi k4m1k4z3,
The script blocker in avast! doesn't block web sites. It is meant to block certain types of malicious code that might be present on a web site. You can monitor it's activity by opening the On-Access Protection Control then, in the Custom settings for the Script Blocker, click the advanced tab and check the box to Show Detailed Information on Performed Action.
There is an option to block URLs in the web shield. The default installation leaves this blank, meaning no URLs are blocked unless they are added by the user. You can check this by clicking the Custom button in the Web Shield On-Access Protection Control.
If there are no URLs listed in the blocked list in avast! then you may have a hosts file preventing access to certain sites or you might have a program like Spywareblaster preventing access.