Then your router is being weird. :( Are all computers on auto?
You'll have to access the router config (
http://192.168.0.1 or
http://192.168.1.1) and dig around in the network settings for DHCP. Kind of hard to come up with a solution, 'cause I dunno what's actually wrong with it. I'd try to clear any DHCP leases on the router, but I dunno how your router does that and stuff, as I have no access to it. Maybe you should just reset it to factory default settings, just keep in mind you'll have to reconfigure wireless security.
Or you could set an IP manually, like I said before. What's your current LAN IP? (use
start > cmd > ipconfig to check)
It's probably in the 192.168.0.x range, or the 192.168.1.x range. Just change the x to a random number, like say, .100 for the laptop, and .101 for the other comp, etc.