Hi Mr Niceguy.
There are a couple of things to check here:
1. Check that the Internet Protocol (IP) address range of your router is set correctly
2. Check that the local IP address of the computers are set differently
To check the IP address settings of the computers. Do the following:
Click on the start menu, then select run
In the window that pops up, type cmd and press enter
When the command prompt appears, type in ipconfig then press enter
There is a line that will tell you the IP address of each computer
If they turn out to be different, then I would suggest checking the linksys website for a router firmware upgrade, as this maybe a known issue to them with that particular router. If you read the release notes on each version, it will tell you of any issues that the new firmware fixes.
Be sure to follow the instructions carefully when it comes to upgrading the firmware. If you do it incorrectly, or update it with the wrong firmware/version number, it can render the router unusable!