MacBook Pro only stays on for less than a minute
It could be something as simple as you power button is stuck, forcing it to shut down.

If you hold the power button for 10 seconds it will forcefully shut down the computer.

In that case it will make the tiny clunk noise, which is normal due to HD been turned off and the HD reader head dropping. Do not do this to often, since you might damage it.

The stuck power button happens to computers on the back seat of the car exposed to food and other stuff.

If the hard drive is dead, you will see a gray screen, and that bad hard drive would not turn off the computer.