lets say the router is 192.168.0.1 subnet mask 255.255.255.0 and your DNS is 4.2.2.2
instead of having the desktop use DHCP (obtain address automatically) code it in 192.168.0.2 255.255.255.0 4.2.2.2
A
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Go into your internet gateway/router/whatever (the device the is responsible for handing out DHCP leases) and exclude a range including the one you just statically assigned. That will make sure it doesn't accidentally hand the same address to another computer - no fun when that happens.
I always have ISC's DHCP server ping before handing out.
Oh, yeah oops, I forgot, we aren't using a "proper" dhcp server here probably.
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