It's to quick to be an overheating problem.
This points to a short circuit somewhere, or an open circuit.
UNPLUG THE COMPUTER!
In the open circuit case, make sure that the power cable from the PSU is currectly and securely connected to the motherboard.
There is an open circuit failsafe in the PSU that causes it to shut down if there is no motherboard connected or there is no CPU installed.
The failsafe prevented any damage.
The first eventuality is much more serious.
There is a short circuit somewhere. It means that there is something broken that will need to be replaced.
Visualy inspect all cablings to see if there is damaged isolent.
Severity: benign. You can use some electric tape over any damaged whire.
The failsafe of the PSU should have prevented any damage. You are lucky.
Start by unplugging ALL power cables to your periferals like hard drives and PCIe card(s).
You now shoupd have only one cable going from the PSU to the motherboard.
Do a test startup. You should see a message about no disk or no system disk.
If you still can't start now, it can mean that your PSU is dead, or the motherboard is shorted.
Try another PSU. If you still can't start, your motherboard is dead. Time to get a new one $$$
If you can start, it was the PSU that died with an internal short or some other fault. Get a new PSU with about the same power rating as the old one.
If you can at least get a post screen, there must be a problem with a periferal.
Start with the drive containing your OS.
Plug back the power cables one at a time and see if the computer can start up at all.
If you find a component that cause you symptom to return when it's connected, that component is dead from a shorted circuit. You need to replace it.
That periferal could have caused some damage to the motherboard or other component. You can loose some performance or be more crash prone. Check everything else toroughtly.
Electro
April 2011