Console doesn't turn on. The power light flashes for a brief second.

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.