So, with the Start button disconnected, does the computer behave at all differently from when the Start button was connected, or is it just the same?
There is one more way to test the Start button. With Start button disconnected and the computer connected to a power outlet, reconnect the Start button for only a brief moment, not more than 4 seconds, then remove it. This would be like pressing the button, even if the button is actually stuck in the ‘pressed’ position. Does the computer start? If so, install a new button. If not, the problem is elsewhere.
I’m afraid I have no other suggestions for fixing the problem. I hope this solution works for you. Good luck.