Computer wont turn on when video card is installed

Ok heres what i got. 2 days ago my comp goes dead. hit the power button and the power led blinks for a minute, the fans kick on for a split second then nothin. No boot up sound/beeps nothin. So i tested the power supply at the 24 pin MB connector, all had propoer voltage, jumped pin 15 and 16-fan turned on. Tested the power switch by jumping it, same led flashes fan kicks for a second and nothin. After playing with it for a few i removed the video card. Hit the power and shes fires right up. Replace the card, nothin. Remove it fires up perfect.

Now theres no obvious damage to the port where the vid card plugs in or to the card itself. But when i took it out the card, its fan was completely caked with dust. I suppose it was not cooling properly.

So the big question

If the video card has overheated and burned out could that cause the whole computer to not turn on?

Or is it more likely something on the motherboard is damaged?

Thanks for your help