This could be caused by a hundred things, But I always start simple.
First thing, try resetting the bios, some computers will fall into a loop if it thinks its suppose to be booting from LAN or other hardware thats not present. You can reset the bios by locating the battery on the MB and disconnect the power from the wall , remove battery, wait 20-30 seconds, replace the battery, hook up power.
Second find where the power button hooks onto the MB and disconnect it, try tripping it manually to see if it is a problem with the switch first.
More than likely this is not the problem, but like i said, start simple. Second, make sure that none of the wires inside the case have accidentaly rubbed the insulation off on a fan and shorted out, also do a check to make sure a wire is not shorting out on the case somewhere. Next, thing will take a while to do, you are going to have to surgically remove components one at a time, this includes the video card, memory or any other add on cards that you may have and try turning the computer on to see if it may be one of the components causing the PSU to fly its protection switch. Removal of some of these components will stop your computer from booting, naturally, but it will let you see if the PSU continues to run or if it does the continual loop.
If none of these solutions has given you any relief then you may have a PSU problem. You may have to test it, or if you dont have the lux of a PSU tester, then you can unplug the psu, give it a couple of seconds to bleed off the caps, use a peice of wire to jump the green and black wire on the large MB connector,WARINING(your must have this PSU completely removed from the system, it cannot be attached or connected in any way to any computer components). If the PSU fan runs flawlessly and you have tried all the other troubleshooting items that I have given earlier then you have either a CPU, Mb, or memory issue.
At this point i would feel comfortable with trying the PSU in another computer to see if it works. If not, then you have the annoying task of deciding if its the MB or CPU. To do this, you would have to remove the CPU and try the mb again, of course the computer wont boot, but if you hook the power to the mb and the psu runs then its your CPU.
Good luck and happy troubleshooting