You don?t give us any information about your systems or your modem. You say that you don?t think the desktop has a network card, so how does the cable modem connect to it ? by USB (the only other choice)? If so, there may be a way to easily accomplish what you want, depending on the make and model of your modem.
Some modems, such as the Motorola SurfBoard models 5100 and 5120, support simultaneous use of Ethernet and USB; some other makes do not support this -- check the manual for your modem. If it is supported, you should be able to keep your desktop on the USB connection, connect the Ethernet connection of the modem to the WAN connector of a wireless router, and both of your systems could use the Internet. There would be no networking between the two computers. I have never done this myself as I use strictly Ethernet, but I have seen postings of people using both USB and Ethernet simultaneously in direct connection. Also the Motorola manual diagrams a system with one computer connected to the modem via USB, and an Ethernet switch with multiple computers connected to the modem?s Ethernet port. Off hand, I see no reason it shouldn?t work the same with a wireless router/switch. Perhaps Bob knows of a problem with this.
As for cost, around here we can usually get a D-Link DI-524wireless router/switch for $20 after rebate; I use both the SurfBoard 5100 and the DI-524, and am quite happy with both.
I?m not sure why you do not want to have the two systems networked, unless they are used by two different people, and you want the highest degree of privacy between them. Otherwise, I would think networking would be advantageous in several respects. But this is your choice. If, in the future you should decide you do want to network the systems, all you would need to do is remove the USB connection to the desktop and make an Ethernet connection from the desktop to the router.
Hope this helps