I once had a similar problem with a server. Once you pressed the power button it would try to power up and then just shut down before it could boot. I took off the case and it turned out that the plastic cover on the power button was sticking, so that when you pressed it, it stayed pressed in and shut the machine off. I broke off the cover of the power button and it's worked fine since. To be honest if this happened to you after it had already powered up and was working it is unlikely that it is the same problem, but it might be worth a look just in case.