|As StuartS advised it is definitely possible to share the laptop internet the way you describe. Simply needs a CROSSOVER ethernet cable to connect the LAN ports of both systems, and enable ICS in the host system. I believe ICS will automatically assign the host LAN connection with IP 192.168.0.1|
You would need to manually set the IP in the client ( desktop) system to say 192.168.0.2 with 192.168.0.1 set as gateway.
You would need to ensure that your router is not using or allocating either of those addresses.
In my situation I have a Dlink router that natively used 192.168.0.1 as it's own address. This was fine until I tried to set up ICS in one of my wireless client systems to attach an Xbox. ICS in windows can only configure using the .0.1 address in the host LAN. I had to change the router address and used a different IP range to avoid the conflict. This wasn't a problem as I do not use static IPs in my network.
If you use static IPs you may find you'll need to reconfigure every client to accommodate the new ICS connection.
The simpler (and cleaner) answer is to make the desktop a direct client of the router as suggested by StuartS if at all possible. Either run an ethernet (Patch) cable from desktop to a router LAN port, or install a wireless NIC in the desktop system. That can be as simple as a USB wireless dongle or a PCI card. Neither of those are too expensive and would give you the ideal outcome.
Goin' Fishin' (Some day)