Unfortunately the AHT is not always definitive but it's a good start. If your MacBook and the JVC Cam Corder both can not "see" the firewire port on the mini, it's possible the port is not functioning. As another test, try hooking both your mini and the MacBook via the firewire ports and see if you can use Target Mode.
Link
Is your mini still under warranty? Apple care? If it is, you might consider either taking it on in or give support a call.
Regards.