Video card dead?

First a question, how do you know that your power supply and the rest of the components of your system are fine?

If you are basing your assumption of operation on seeing the power supply fans run, and the drives perform their POST, that is only a partial check.
You need to verify ALL of the voltages that the power supply generates are at their correct levels under a load.

As to the fan on the video card, it depends on how and where it gets it's power from as to if it is dead or some other part is dead.

Do the blades of the video card fan spin freely when you spin them by hand?
If not, it is possible that the bearings in the fan failed causing the GPU to overheat and the video card is now locking up the system bus.

It is just as possible that a failure of a power regulator on the motherboard is the cause.

Look at the motherboard and video card for burnt, bulging or leaking components. If you find any, that is a clear indication of what has failed.

Otherwise, you need to try the CPU and video card in a different motherboard to verify if they are working.

Chas

Confirm the proper operation of the power supply
before you replace anything. If the fan on the
video card doesn't turn, that points to the P/S
No beeps means no power. The video card has to
unload first to the CPU before the Cpu can boot.

You can test your power supply independent of the chassis. I did this a while back but I can't remember the pins on the motherboard connector that need to be jumped with a small wire. If you do a google search for power supply connectors you can probably figure out which to connect and then you'll be able to fire up the power supply without a chassis power button.

I would guess power supply before anything else. It's the least expensive of the components to replace (for the most part).

An unlikey, but obscure one I once had of these...

The video card has multple video out systems. By default these are set to clone the image at boot if detected. If there is some dirt/dust in the connector then it may be (not) detecting the output device (ie monitor, tv, AV-out, etc) and defaulting to another port/device.
In a similar manner, if your motherboard has onboard video the bootup may be defaulting through the other video card.