Welome and congrats on getting started! The reason you can't connect to the AP when the desktop is connected is that only one client can be connected at a time with the same MAC ID. As for what you can do about this, the best way would be to send a disassociate packet for the dektop, taking it offline temporarily, and then quickly connect with your spoofed MAC. The AP will believe the desktop has simply reconnected and then you're all set!
Good luck and happy hacking. Just make sure you are being safe and not beraking any laws/TOSs/EULAs etc.