avast does not have a built-in firewall. Just an antivirus and antispyware.
Which firewall do you use? Is ashWebSv.exe allowed to connect?
If you really knows what you're doing making an exception for this game, use the Exclusion lists:
For the Standard Shield provider (on-access scanning):
Left click the 'a' blue icon, click on the provider icon at left and then Customize.
Go to Advanced tab and click on Add button...
For the other providers (on-demand scanning such as the screen-saver or the Simple User Interface):
Right click the 'a' blue icon, click Program Settings.
Go to Exclusions tab and click on Add button...
You can use wildcards like * and ?.
But be careful, you should 'exclude' that many files that let your system in danger.