No video on internal nor external display

A few days ago I started up my iMac (21.5" / Mid-2010) I felt the fans running, heard the boot chime and everything seemed fine except there was no video, no backlight, nothing at all on the display. I pressed the play button on the keyboard and iTunes started and played a song.

So I restarted the computer, did the SMC reset, connected it to an external display but still no video.

I checked the diagnostic LEDs and found that the first two are on, but LED #3 is off. So I reseated the video card (as the technician guide suggests) and retested. But still nothing.

My question is, how do I know for sure whether I need a new video card or a new logic board?