Hi you there ...
My first reaction to this would be to think that your graphics card is faulty. If this is a desktop machine, then this is easy to check - just swap in another one. If this doesnt work then perhaps a motherboard issue.
If this is a laptop then Im afraid it will need to go to a repair shop to replace the parts - unless you are confident in your abilities to replace the inner workings.
With it instantly powering down, it seems the machine is not getting past the initial "Power On Self Test" (POST). This can be caused by a bad graphics card, but is more often motherboard trouble.
You dont mention any beeps coming from the machine. This could be because no internal speaker is attached, or that it doesnt even get this far in the POST but could help with diagnosis if you just havent mentioned them (how many beeps? is it a repeating pattern of beeps? ...).
For this next bit ensure you take proper anti-static measures (and photographs if possible).
It might be worth removing everything from the motherboard that isnt needed. This will discount anything else that might interfere with boot. What you need is the processor and fan (make sure the fan is turning), at least one stick of memory, the power supply, a graphics card, a monitor, and the power button connections. If you do remove them make sure you make a note so you know where to put them back. If it boots now (you will get an error message on the monitor to say there are things missing), then replace the things one at a time until you find the one that causes the machine to not boot.
Please let me know how you get on.