Hi Samuel!
First I would open up the PS3 and clean everything inside. Also take the power supply out and clean it completely.
Guide: [guide|3231] (You will only disassemble it, not replacing the motherboard obviously).
After this assemble it again and see if it works! If not, then most likely the power supply need to be replaced. But lets try cleaning first!
If you have any questions, please let us know!