I have that same problem, but it is probably not your
problem - I know what mine is.
My tower case is an old Gateway (+10 years probably!).
When I press the power switch, it clicks and it is supposed to make the connection and pop back out. Trouble is, it doesn't always pop back out so it equates to being pressed in all the time or just holding it in. It runs for about 2/3 seconds and shuts itself off.
XP never gets a chance to boot.
I have dedicated a nice sharp pocket knife with a good point on it that I can pry out the edge of the button until it snaps back out, ready for another go.
Then if you are real careful and lightly push it in just enough to make contact, but not click, it will not get stuck - works every time, but requires a certain finesse that only I have mastered. Every once in a while I miss it and have to knife it...
The good part is, nobody is able to turn on my computer, so it doesn't get messed with.
Someday when it breaks for good I will swap it with my never used reset button.
So, maybe your power button is about to be defective.