Okay. Usually when there is an issue like that it something simple. The first thing that comes to mind and the easiest thing to mess up are the little cords going from the power and reset buttons to the motherboard (its actually usually the USB ones that get plugged in backwards, not the power/reset buttons themselves).
These cords are often tiny, poorly labeled, and easy to mix up. Second most common problem in this case, drawing too much power (I doubt this; your power supply was fine). Third (and this is fairly rare) is shorting out so the system is powering down. I'm going to give you some extra steps than are probably needed, just to make the trouble shooting process easier in case it isn't number issue #1
I am curious; does your computer beep at all, and if so, how many times? Is it rapid? Long? Normal sounding? Short and long? Etc.?
I would start as follows:
Unplug to power cords as follows:
...from your video card
...from your harrdrive
...from your DVD drive
Now, turn your computer on like normal. You will probably hear a series of beeps that sound abnormal; these beeps are probably telling you that your harddrive, etc., are unplugged.
If the computer does not turn off on its own, plug the video card in and try again. Then repeat with the CD/DVD, etc., until you find the issue.
If the system still turns off on its own, and it probably will, we want to look at the front-panel cords next. We want to unplug everything -except- the actual power button. Double and triple check the power button is plugged in right. Try again with turning the computer on. If the system turns on you want to one-by-one double check the front-panel cords. Start with the reset button. Then move on to sound if you have it. Then finish with the USB.
From there, plug the GPU back in, then the CD/DVD, then the harddrive. As you do this process the beeps on startup will likely change.
Now, if you get down to only having the power button plugged in and you STILL have issues, pop back on here and let us know. There's still lots we can help you sort out.
If you like, I will also be on g-talk. ewtuthill @ gmail . com and you are welcome to chat with me (just let me know who you are, so I don't ignore you! lol)