What is the color of the Mag-Safe plug Green or Orange?
Are you up to doing some digging here? I would start by opening up the system so you can disconnect the HD SATA cable.
Your symptom sounds like you have power, just that the draw is to great so it shuts down.
If the HD has died the motor can short out so by disconnecting the HD we should see a different response when you start it up again.
If you have an external HD FireWire or USB with a bootable OS present on it you may want to give that a try after you first see if it tries to startup.
Please let us know what you discover - Good Luck!