I'm an idiot. I had my Famicom twin system for about 10 minutes before I fried it. I knew I couldn't plug my NES ac into it but I had my Toploader and my AV Famicom plugged in side by side and I unplugged the wrong console and ended up breaking my Famicom Twin.
I found an earlier post that suggested that when this happens to replace the main cap (which I could tell I blew) and the power regulator. I replaced both those pieces and now I got the power light to turn on (it stays on all the time) but nothing ever comes on the screen.
Any advice on what else I should try next?