Normally you can access your Airport card settings and turn the device on or off, either in the System Preferences or in the system menu. Upon updating to Snow Leopard, however, a number of users have noticed a problem where their Airport cards will not turn off if they're on, and others will not turn on if they're off.
Both laptop and desktop computers seem to be affected by this problem, and some have questioned whether or not it's a hardware issue that has cropped up; however, the devices to seem to work normally if they're enabled, and resetting PRAM and SMC settings do not seem to affect the problem. Despite this, if you have a hardware problem such as this I do recommend you try a PRAM and/or SMC reset as one troubleshooting step to take.
More than likely this behavior is a driver issue where the system settings that are supposed to control the airport devices are not properly communicating the power commands to the device. This could be due to a bug in the drivers, but since most models similar to those affected do work properly the more probable cause is a faulty preference file that's associated with the Airport settings.
To tackle this problem, first try deleting the following plist files from the /Macintosh HD/Library/Preferences/SystemConfiguration/ folder:
If after deleting those preferences and restarting the computer your Airport card still neither activates nor deactivates, try removing the "preferences.plist" file from the same directory and restarting again.
Alternatively, you may have success by creating a network location. Doing this will rewrite the relevant network preference files with alternative configurations that will be loaded independently when you switch locations. Therefore, one easy step is to go to the "Network" system preferences and choose "Edit Locations", and then click the "+" sign to add a new location.
From here there are two options: Keep the new configuration and set it up accordingly, or remove it and go back to your old one. Doing the latter may be easiest, but may also leave you where you were originally. However, in creating and deleting the new location you may spur the Airport preference files to behave correctly. To delete the new location, first click "Apply" with it selected so the system switches to it, and then edit the locations again and remove it, clicking "Apply" again with the old location selected.
If you choose to keep the new location (which I recommend), set it up with the same settings as your previous one (ie, the "Automatic" one) and click Apply.
After you have altered these settings, restart the computer and then try your Airport settings again.