So the scenario is as follows:

You have two desktops and a laptop. The two desktops receive an internet connection, one via wireless. The non-wireless is plugged into the router via a network cable.

The new laptop won't receive a network connection regardless of whether its plugged into the router or using wireless? When you plugged it into the router, you sure you plugged it into the correct port?

Can you confirm that, when the laptop is plugged into the router, that you're not getting an IP address?

Your winsock may have somehow got corrupted. For XP there is a utility you can download to fix the Winsock but I'm not sure if anything exists for Vista. You can try this though....

1. Click Start. In the Start Search dialog box, type: cmd, and right-click cmd.
2. Click Run as administrator.
3. Type: netsh winsock reset, and then press the ENTER key.
4. Type: Exit and press ENTER.
5. Restart the computer

Also go into "network connections" and verify your connections arn't actually disabled.

You also say you're router is not working? Make sure you're modem is plugged in to the correct port.