You said it happens to the computer connected through the router. If you remove the router and plug the computer straight into the modem, do you still have the issue?

You may also need to get the DNS numbers from your provider and add them to your connection.

"You need me. You wouldn't be much of a hero without a villain. And you do love being the hero, don't you. The cheering children, the swooning women, you love it so much, it's made you my most reliable accomplice." -- Lex Luthor to Superman, Question Authority, Justice League Unlimited