My Dell Inspiron 5567 (i5 7th gen 8 GB RAM, integrated Graphics.) (2 year old) does not start at once. Once it does start everything works normally (Like it did when it was brand new). Problem is, its power button behavior is abnormal. It sometimes starts at one go other times I need to press the power button like 50 times to get it started. I got it checked from Dell Authorized center they say power button is not at fault.
No repairer is able to say anything satisfactory. I only get "May be" and "Could be".
If it won't turn on when the button is pushed, and it happens both when connected to the charger and when on battery only, then it sounds like a bad button to me. The only thing I would suggest is either going with what some do which is never turn theirs off (not an advocate of that but some do it) or get the button replaced. However, if you choose to have it worked on, I would find a different tech than those you have spoken with so far.