As I was beginning to get desperate to use both my printer and my wireless card (An Abit AirPace WiFi), I roamed the web to try to find a way of solving the issue. It also solved a problem with my Abit µGuru power management system. Although Windows 7 recognized the hardware and Action Center directed me to the correct download sites, the drivers wouldn't install because they weren't signed.
OKI B2200 and printers from the same series don't have drivers that are officially listed with MS yet, so the problem here is apparently also that the driver isn't signed. Here's a workaround: Install Unsigned Drivers on Windows 7 & Vista with Driver Signature Enforcement Overrider
My hardware now works perfectly. However, since driver signing is an important security measure, this is an issue that should get some attention. Some of my hardware comes from Abit, which is now bankrupt and will never pay MS to have old drivers signed. With Windows 7, apparently, one has to check if the hardware is listed in MS's driver database before one can safely buy new stuff.