From the good testing you have now performed, you can be certain that either:
(a) your external iSight's connection is not working, or
(b) your external iSight itself is not working.
Testing your external iSight on other Mac(s) can eliminate the (b) possibility. If your iSight cannot be recognized as a Firewire device by any Mac's System Profiler, it needs professional service. Your Apple-Authorized Service Provider can tell you whether it will cost more to service your external iSight than to buy a compatible USB webcam like those described here: http://www.mac-compatible-web-cam.com/
When you test your mini, connecting to the FW400 port on external drives cannot help you. External iSight does not like to be daisy-chained. You should disconnect all other Firewire devices while testing your external iSight. More testing suggestions here: http://www.ralphjohns.co.uk/EZJim/EZJimpage4.html
If your external iSight can works with any other Mac you test, you will next test your FW400/800 adapters or cables. If the other Mac(s) you use to test your iSight have no FW800 port, you will need more than one FW400/800 connector to do the test on your mini. Proceed as follows:
• Shut down (not "Restart") your mini. Wait about 15 seconds. Then power-on mini.
• Connect and test your external iSight with a different FW400/800 cable or adapter. If neither connection you test works on your mini, try a third adapter or cable.
• If you mini's System Profiler does not recognize your external iSight with any connector you test, ask your Apple-Authorized Service Provider to test whether your mini's FW800 port needs repair.