network set-up

Clarifications

the desktop needs a wireless card too. Can't help with the VPN thing.

If you want to setup a Workgroup you should have both computers on the same side of the router and then if you are using some form of Windows run the Network Setup Wizard to setup your Workgroup. You can have one computer connecting by WiFi and the other hardwired to the router but you need to remember that the WiFi connection will be slower than the wired connection so if you are planning on moving large files about you will have a performance issue to deal with.

Col

... NOW you're having trouble connecting between your laptop and desktop, which leads me to believe that they're on the same LAN and that it worked at one time, presumably when both were using wired connections.

Some models of WAPs or Wireless/Routers by default secure the wireless segment from the wired segment, and this would indeed cause the symptoms you're describing. Check the wireless and security settings on your router or access point; I don't recall exactly what that feature is called but turn it off. :-)

You should not have to convert your desktop to wireless, and because of the performance degradation that Col indicated, you don't want to. Nor should you need to worry about VPN. You just need to configure the security between the wireless and wired segments.