Can I FIX it? - Evercade EXP Limited Edition

I got this Evercade off eBay, listed as 'Doesn't turn on'.
Let's see if my dumb brain can work out how to make that not so.
Warning: This video will make you shout at the screen, call me an idiot but at least it will remind you that I'm not an expert in ANYTHING, just someone who is learning by doing. Don't copy me, I mistake a lot.