Power supply checked (original SEGA), got 12.5v DC with no load on the plug, and I was able to follow it to the power switch so the switch is OK. No LED light, no display, nothing at all. It is a Genesis first model, with TMSS. I couldn't find a specific schematic as there's been numerous revisions. I'd like at least a power regulator schematic so I could check and rule out bad regulator or fuse, etc.
There's no fuse on the Genesis. Cherck your LM7805 and see if you get 5v Schematic (part 1) look at the bottom right for the power circuit (IC5 and IC7): http://emu-docs.org/Genesis/mega1.png
Checked the output. It was 0 but when I lifted it and checked again, I got 5v so there's a short on 5v rail somewhere. I didn't find any obvious sign like bad solder, loose part, corrosion etc. That leaves shorted caps and part somewhere in the system.
Last time I had something like, it was the power jack which was corroded and making false contact: I had 10V from the AC plug, and when I was turning the Megadrive on, I get 0V. I'm talking about this jack and this small PCB After removing the jack, found out one of the hole where the jack is soldered wasn't making the via on both side of this small PCB, and I had to solder the lead of the jack on top AND the bottom.