How is it that you are connecting the Dell machine to your LAN?
Are you hardlined in over Ethernet?
Are you connecting via Wireless LAN (WLAN card)?
We need to know that information first. That will determine which connection object in the Network Connections applet we should be focusing on. My first reaction would be to look at the Network Connections applet by doing the following:
Start >> Control Panel >> Network Connections
You should probably see a connection object which is giving you a Yellow icon with a White "!". That is probably the suspect connection object / device. From within the Network Connections applet, you can right-click the connection object and select Status. There should be a Support tab with a Details radio button (or some combination of tab and buttons to that effect), which can show you more information about how the IP configuraiton is assigned to the Dell machine.
You can also gather this information from the CLI via Command Prompt (if you are so inclined):
Start >> Run >> cmd.exe >> [Enter] >> ipconfig /all >> [Enter]
I would do the same steps on the Sony machine since you know that it is having no connectivity issues on your LAN. Compare the information between the two systems and you should notice some discrepancies between the IP address, DHCP server, DNS server, etc.
Post back if you require further instruction.