Asus laptop won't boot

Asus laptop won't boot

I've got a laptop Asus X71SL and it won't boot.
When I hit the power button, the screen stays black and the fan does not spin. The first time I boot it, the HDD led is always on (it does not flash). The next times, the num lock, caps lock and HDD leds are always on. If I unplug and plug the power cord and then start the laptop, only the HDD led will be on. And if I start it again, the the leds will be on. Etc.
I am unable to go in the BIOS, unable to go in GNU/Linux, unable to boot on a live-CD.
I tried to boot without hard drive, without RAM and without DVD drive, wihout success.
I tried to use only one of the RAM sticks and then the other. I tried that on both RAM slots.
I tried with and without battery, without success.
I plugged another screen and no signal goes to it.
I tried to reflow the graphics card.
The only hint I have is that the fan spins when I remove the graphics card (it does not spin when the graphics card is plugged to the motherboard). Does it mean the graphics card is faulty?
What can I do to boot the computer?