If you disable your A/V, and the game runs, I highly doubt that the firewall has anything to do with it.
Usually, a firewall will prevent you from connecting to online servers, not running the game in the first place.
I see that Mr.Agent is trying to help, but I don't know if it will in this case.
First, since I don't know your situation to the fullest, I'd like to ask if you had any other A/V programs installed on your computer recently before you installed avast.
Second, have you applied any patches to this game recently, or checked for patches.
Third, are you sure that the drivers for your computer (video card, sound card, etc) are up to date, and don't have any known problems.
Fourth, I would ask exactly what O/S you are running, with SP level.
After all of that is said and done, we might be able to get a bit further with your question. Thanks!
EDIT
It looks like you run Windows Vista, but I'm looking at these entries:
O8 - Extra context menu item: &Ściągnij przy pomocy FlashGet'a - D:\Flashget\jc_link.htm
O8 - Extra context menu item: &Ściągnij wszystko przy pomocy FlashGet'a - D:\Flashget\jc_all.htm
I'm not sure what they are or why they're there. I'm guessing that it's a download manager, that you wanted to be installed, but who knows. Let us know if you installed it or not.