Hello & welcome, Kino !
But, when I select firmware upgrade, after a few minutes the camera powers off.
Maybe you're waiting 'till the camera powers off due to Canon's power saving ?
Maybe CHDK is loaded & running and the camera is ready, sitting there in playback mode, still waiting...
After confirming the fw update process, do you see the CHDK splash screen ?
--> press (or half-press) the shutter button once to switch to record mode
--> for startup infos & buttons on the A480 see also
CHDK specialities from the A480's wikia page