PC Freezes with Looping Sound

I've tried shorting Pins 15 and 16 as suggested in the guide to get it started, however the PSU doesn't start no matter what I try. I took a good look at the Motherboard connector and noticed that Pin 8 is completely missing.

Do not do that procedure. Defined in my post is what you do. As with any good diagnostic procedure, you disconnect nothing and remove nothing.

Setup to access (multitask to every peripheral (disk drive, sound card, CD Rom, Internet, USB, etc). Then measure any one orange, red, purple, and yellow wire that goest from the power supply to motherboard. The entire procedure should take a minute. And again, disconnect nothing. Everytime you make a change, you add variables and potentially more confusion.

The procedure as was posted here is the best one – the most informative (in part because reason why is not yet apparent).