If you have a software firewall installed it may be clashing with the router's hardware firewall. If that is so, try turning the software firewall and see if the computer will access the server.
I have this problem too between the Zone Alarm and my DSL modem - which has a built-in hardware firewall.
My internet got messed up without warning. Today I was using it, I shut my computer down, turned it back on a few hours later and the internet didn't work. I have 3 PCs on my router and all but mine work. The weird thing is that some programs will connect and some will not. The computer knows I'm connected to the internet and I've run anti-v, spyware scans, and nothing showed up.

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