Hello and welcome to Tom's Hardware Forums.
It might be enough to bring up tyhe Command Prompt and reset a couple of thikngs. In XP go Start to Run and type cmd into the Open box and press Enter. In Vista or Windows 7, using your Windows key and R together brings the Open box up.
At the Command Prompt type ipconfig /renew, press Enter and when that finishes, type ipconfig /flushdns hit Enter and then type exit to leave the form. Restart the computer and you should be able to connect but if you can't, there may be another resident who's system is causing the problem.
All this assumes you have automatic DHCP enabled so if the problem persists, please post back which version of Windows you're using.