Chosen Solution
I bought an untested SNES, and after plugging it in, no light would come on. I took it apart to see if there was any obvious damage, but nothing aside from a little corrosion around the power input solder points which I cleaned off. Now, after that, the light will flash on for a moment when I hit the switch, but will immediately turn off. I’m fairly ignorant towards electronics, (i know how to test for continuity using a multimeter and solder/desolder, but that’s about it) so feel free to over-explain if necessary.
So it appears to have been the shielding not being correctly placed, which was not allowing a proper current ( apparently the shielding has a connection to ground in its design, so not having it on was not allowing it to ground correctly).