Hi and welcome to the forum.
If this is an FP3 and not the FP3+ you may be well out of warranty so if you do not want an official repair, at ## cost then you may want to consider a DIY
Can you still charge the phone, does the LED show charging as yellow or green?
Try to ensure the battery is charged to rule out that as a problem.
It may just need a clean. The power switch is part of a small strip connected to the main board.
You will have to start by removing the screen
Here is the location the long green strip to the left in the image below.
Note: There is no guarantee that this is the problem and you may create further damage by trying a self repair. So this is not advice just a show of the button location and detail
If cleaning doesn’t help it may be possible to replace the strip, but removing it completely isn’t something I’ve tried