Looks to me as if the problem is with your router. Either it is misconfigured or faulty. Looks as if there are problems with auto DNS or with the traffic direction of the firewall. I would try to reset the router to the manufacturer's defaults. Usually there is a little hole at the back of the router into ehich you insert the tip of a pen for 30 seconds at least and press while the router is powered on. If you have a user manual use it. After resetting you will have to set up again your user name and password.
If this doesn't help try to borrow a router from a friend, configure it and see what happens.
By the way, if you are not sure whether sp2 is installed or not enter control panel > system. In this page you will see what version of os is installed (sx or xp sp1 or xp sp2)