Try the obvious first:
- Replace the Ethernet cable if you have one spare (or try the existing cable with another machine)
- Reset the modem/router
- Take the laptop to a friends to find out if its the laptop or modem/router which is at fault.
Have you set the ip address and dns manually? If your unsure, and using XP, go to Start, Control Panel, Classic View, Network Connections, right click on the Local Area Connection and choose Properties, go to TCP/IP settings and choose Properties. Change the settings to let Windows automatically assign the laptop's IP address and dns server.
The main thing is to trial and error to find the problem. Its either the laptop hardware at fault, or software settings, or the modem/router connection (when you connect wirelessly are you sure your connecting to YOUR router?? and not your neighbour's) etc etc etc.