I've just been thinking about this a little...
Before you attempt to disassemble the air valve, try this test.
Withdraw the needle. After you do this, it will release the trigger and the curved lever which depresses the needle actuator when you draw back on the trigger. With these parts removed, there will be nothing at all in the airbrush which should be able to open the air valve under normal circumstances. Connect your airbrush to your air source. If air flows out of your airbrush under these conditions, then yes - the valve is stuck open.
If you are not confident in your ability to rectify this yourself, as detailed in Scott's post above, then definitely make arrangements to return the airbrush to Badger, following the procedure detailed here: http://www.badgerairbrush.com/Service-Supprt.asp