There are a few of these reported on various forums and websites (Google is always your friend) and unfortunately it's often turned out to be the motherboard.
Try taking the top off and locating the cooling fan on the processor. With the top off, turn the PC on and watch the fan. If it doesn't move at all or just twitches then it might be the power supply. If the fan runs for a couple of seconds then stops (which sounds probable from your description) then the motherboard is likely I'm afraid. We can do a few more checks to confirm it but they get a little more involved.
If the motherboard is gone then you can still get all your son's work and documents off the hard drive by putting it into another machine and copying them.
Let us know how you get on and we'll help further if we can