My first thought would be that it's malware related, but if this is a work computer then A) why isn't your company IT people dealing with it, and B) it might be that these sites are blocked at the company gateway. If you feel you have a legitimate reason for going to them, talk to your boss and have them talk to IT.
If you own the system, I would suspect malware more than a firewall. Firewalls, contrary to popular misconception, don't really do site by site blocking/filtering. They either allow packets on a specific port to come through or they don't, that's really all firewalls do. Think of them like a bouncer at a club, and they decide who gets in and who doesn't. There a whole host of things people think firewalls do that they don't, but that's another topic for another day.
My thoughts would be it's either malware related, or you've installed some anti-spyware app that tries to use the HOSTS file as some kind of blunt instrument.
New computer with Vista Business will not connect to some sites, cannot download or update some programs. Computer will not connect with some servers. But others sites are allowed to connect and download. Is this a firewall problem? I have checked settings to allow open port but still does not work. Suggestions please.

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