yeah, you can momentarily short the two (+ -) mobo power on pins carefully with a screwdriver
so, you are thinking your case power button is bad?
personally, I would repeatedly pull in and out the 24 pin atx connector and the aux +12V 8 pin CPU connector, after spraying contact cleaner in/on them - then blowing them off with air spray can.
Also make sure you are plugging in CPU fan to 4 pin cpu connector - not a 3 pin. The FAN doesnt have to be 4 pin - but the mobo connector you are using does
I would also take out CPU and look at ziff socket pins extremely carefully with a 3" round 5X magifier from dif angles to look for bent or missing pins
@ OP
Any time you ask a question like this it should be obvious to list your entire system. I would like to know what HS you are using - some backplates short out on mobo exposed devices/solder blobs