Goats, or no goats, this isn't working but at least now I know why.
Every time, I'd get the no post, no beeps error and every time, I'd open it up to see a handful of bent CPU pins. And every time, I'd straighten them out (the credit card method works surprisingly well), only to see them bent again. Apparently, I was bending 'em by pushing a little too hard on the heatsink. The restraining clips are VERY difficult to attach (it's seriously a very tight squeeze and a very slim margin of error), and even harder to detach. So naturally, I'm using quite a bit of force getting it clamped down and unclamped. So, that's mistake #1. (Apparently, using a screwdriver is a must)
But last time, I miraculously got the heatsink on without bending any pins. No beeps, no post as usual. I'm almost certain it's the CPU. Even though I did try to be gentle with it, it's possible that it's down for the count.
Going to try a replacement CPU as well as a replacement heatsink (preferably one that's a lot easier to attach)
But at least the good news is that I'm really good with thermal paste after having to apply it and wipe it off so many times. (Grain of rice + spreading around with one of those tiny grocery cards method)