My FP4 power button was working less and less and then not at all anymore. Unlike quoted here, I think it is meanwhile a common problem.
The solution and repair is simple in case it is the same problem I had and it is shown here on YouTube.
You just disassemble the phone completely including removing the motherboard. Then you will find corroded contacts that you can clean and it will work again.
NOTE: as FP support seems completely unresponsive and did not react to my ticket for 2 months(!) the 5 year warranty seems currently worthless. So I quickly fixed it myself.