Webpage display problem

I have a desktop computer running windows xp. a friend passed away and his widow gave me his computer which also runs windows xp. I wanted to check it out so I connected it to the internet through my router using a wifi adapter. I decided to open a twitter account so I did it using his computer. I also visited a few websites. When I was satisfied that it was fully functional I disconnnected it. Now I cannot connect to twitter or this other site with my computer. when I click on the link I get this screen saying" cannot connect to the real twitter.com" or cannot connect to the real website .com. If I connect his computer back up I can connect to these sites with his computer only. Anyone know what I can do to connect to these sites with my computer? thanks for any help

 

Hey al, shutdown your computer, wait 10 seconds the power it back on, then start tapping the F8 button the same as you would do to get to Safe Mode, when the black Advanced Options screen comes on go up to Last Known Good Configuration and hit Enter, then wait and try to get to twitter.

 

Thanks for the idea Nick but it didn't work. This is some sort of network issue I think . there is so much security involved with a twitter account it's as if my computer is returning the wrong network protocol when trying to log on or a router issue since the router is now out of the loop. I can't figure it out