Well what u have here is called the yellow light of death or also called (YLOD). Here is a couple ways to tell if it is a power failure or the motherboard malfunction. If you listen carefully well you turn on the system if you hear the fans turn on then the system turns of after a couple seconds that is a motherboard malfunction the system will realize that the system is broken. But if you turn the system on and the fans do not spin and turn on then you have a power failure. That could happen when your power cord/the AU 3 pin power cable gets damaged. Another way a power failure could happen is when the power from the power cable can't pass through the system and reach the main power circuit. But you got lucky there is a way you could fix this. You could get the PS3 repair kit and fix it yourself if you are good with hardware or get a good repairer to fix it for you.
To fix it yourself, visit youtube.com and type how to fix ps3 yellow light of death.
Watch and follow the instructions in some of the videos and you will be able to fix the issue.