PC failing to boot

Hi i've been having an awful issue with my pc the last week or so and I can't find a solution. my pc is failing to even boot which is frustrating to be sure what the problem is. my pc sometimes shows it's recieving power by the led fans turning on but only for a second or less before shutting back down. i've tried resetting the CMOS by using the method of the pins on the motherboard(clear CMOS) as well as taking out the motherboard battery momentarily to see if that would work.(these were suggested methods when i searched my problem on google) i even tried unplugging the cases power button plugs for the first time ever and i then noticed that the one labelled "POWER SW" only has one metal prong on the motherboard for the switch to be plugged into while that power plug has two holes. is this by chance normal? if not i imagine that would be my problem. to go along with that point, after leaving my pc off and unplugged for about a day i plugged it back in and turned on the power supply switch which immediately turned my pc on for a second without even touching the cases power button which is very odd. i feel like my motherboard has failed and i need to purchase a new one though i don't want to spend the large amount of money without being sure the motherboard is my issue. I provided a picture of the "missing prong for the power switch" which is toward the bottom of the picture.(you can see along that white strip of prongs which is where the power switch plug, reset button plug, etc that the first prong is missing.) Please someone help me and respond with some knowledge that may help fix my unfortunately broken computer, Thanks :,(