Can't start computer

How do you know the graphics card is dead. I had a similar problem where display wouldn't turn on, but i would get power leds. Try reseting your motherboard by pulling the plug for the outlet and then pushing the power on button.
ROger

Try physically removing the AC cord(wait 1 min.), reseat and then try a power-UP. If the problem persists, then likely you have a power supply problem. With case cover off, observe the fans, they may spin or not or at least move abit, then a power problem. Understand, the system uses a logic relay circuit to trip the p/s unit ON, but if the circuit is screwed-up it can't or simply has failed on its own. Cheap or low-wattage p/s units can cause similar results due to stressed p/s or being cheap., thus replace with a higher wattage unit plus make it a namebrand. However, this doesn't exclude any possible secondary problem since a stressed p/w can cause other componets to be stressed or fail, it just doesn't become a simple p/s replacement, beware of that.

tada -----Willy

How about the fan on the CPU's HSF, and the fan in the power supply?

If you're lucky, it may be simple as that. You get any beeps (you may have to check your motherboard manual to check what the beeps mean.) Do you get an "out of range" error message when you boot, or just total black monitor?
Have an extra video card to test your system with? The possibilities are many. Good luck.