So, I finally have an answer to my own question! Turns out it was a bad power switch, well not "bad" but it needed some cleaning.
I got two GBA units in from Japan with the same problem, great battery terminals, working fuse but no power at all when switched on. I did notice that the blue unit would flicker power when I switched it on and off. So I slowly moved the power switch and at about 55% on, the unit would power up and the games would play.
That got me curious, so I took the pink unit (since it wasn't working at all) and opened up the power switch. [http://www.fillharttech.com/wp-content/uploads/2016/07/IMG_20160721_232620.jpg|You can see what it looks like here.] It's actually a pretty simple design. There are three metal contacts and the slider has two very tiny metal prongs that contact only two of the three pads at any time. In the provided picture, inside the slider, you'll see those three metal pads and they look very dingy. I took a small piece of 600 grit wet-dry sandpaper and cleaned up those three areas. I also lightly sanded the slider as well.
When I reassembled the pink unit, it powered on like a champion! I was very happy to have found the issue and jumped right onto the blue one and gave it the same treatment. Sure enough, the blue powers on with no issues at all. Both units work great after I gave it my typical cleaning and further refurbishing. I almost want to keep one of them just for the satisfaction of solving this mystery.