I'm sorry ZX! It was my fault!
Everything works fine! :-)
This morning I started the Mini, then I unplugged the display power cable. Then during the day I restarted some times OSX.
And in system profiler, graphics/monitor section, I noticed that graphic card was listed, but no display was detected and listed: I think that in this case Quartz Extreme is disabled.
This evening I plugged the display and restarted OSX, the display is now listed, and iMovie starts correctly.
I need to unplug the display power because I have an old 22" Apple Cinema Display with the old ADP port (but it still works, image is still bright and almost perfect ;-) so I want to keep until it explodes! ;-) And I have an Apple active ADP to DVI converter. The DVI is then connected to the Mini with the included HDMI-DVI adapter. Actually I'm not able to power off this display, not even with the touch button on the display chassis. So when I'm away from home and I want to remote control the Mini, I don't want the display on all day, I know the monitor stops after some minutes, but I want it always off to keep it the safest as possible.
I thank you so much for your help!
And very good work guys! :-)