You might try clicking Connect To (or Control Panel, Network Connections) Show All Connections, then select the appropriate connection, go to Properties, TCP/IP properties and make sure that IP address is obtained automatically and that DNS server address is obtained automatically.
While you're at it make sure Firewalls are Off (Windows' firewall is under Advanced properties) until you get a reliable connection.
If using wireless and you know how to address the router, also turn off wireless security until you have a reliable connection.
We have about a 5 year old Dell P4 running XP. It connected to the internet briefly and then the connection failed. Everything I have tried has not worked. Tried: new network connection, repairing it, reinstall driver. remove device from device manager and reinstall, swapped out network cable, swapped out network card etc. The wire and the jack check out. the other computers get on the net. I am baffled. Any suggestions?