QUOTE
even though the problem computer is not connected to router in any way
How do you stop them wireless connecting? Are you removing/disabling the wirless network card?
This is not a restriction of the ISP is it? Some ISP's do not allow multiple connections. ( but you say the wireless laptop connects OK?)
You didn't answer my question about assigning IP addresses - help us to help you by providing information when it's requested please.
What are the operating systems on all the PCs? Open a command window Start>Run type
cmd. In the black window that opens type
ipconfig. Write down the results or take a screen print. Do this on all your PC's and laptops. Post the LAN addresses and Gateway addresses here.