Does your firewall prevent you from going online?

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For awhile after I installed my AOL firewall I had difficulty going online. So, I dumped AOL and switched to broadband. Now, I can get online almost everytime without any real issues. But, there are times when my broadband will mysteriously go out for no obvious reason. And, I was wondering if it's possible that the new firewall from Comodo is blocking the broadband connection. Does your firewall give you trouble as well and keep you from making an Internet connection? How can you program your firewall to know which sites are acceptable?