Yes - as it's acting stone dead trying to start it by jumping the pins vice using the switch is the next logical step.
It would not hurt to also check that the switch works with a multimeter and to do the same for the reset switch.
Using a known good switch would also work. It does not have to be installed in the case.
The ATX Power and Reset switches are the same kind of switch (monetarily closed) so you can use the Reset switch in place of the Power switch by putting the Reset wires on the Power Switch pins.
Those are both usually plain common 2-wire switches. It doesn't matter which way wires are so long as they are on the right pins.
In other words 'plus' and 'minus' doesn't matter for Power and Reset switches. And you can use those two switches interchangeably.
(Does not work with older AT switches.)
I flipped the orientation around and added color to earlier photos and screen shots to make the pinout easier to follow.
Pins_1.JPG
I put the markings were the actual pins should be, the connectors obscure some of them because of their slant.
Don't let that confuse you.
Sorry I'm slow. I had a medical thing today and I had to sleep off the meds or I'd talking a language previously unknown on earth.
.
GRUMPY OLD FART - On Hiatus, sort'a
Mann-Made Global Warming. - We should be more concerned about the Intellectual Climate.
You can teach a man to fish and feed him for life, but if he can't handle sushi you must also teach him to cook.