a standard 13.8v dc power supply should be fine.
they are widely available in maplins ect.
the alternative would be to repair the original power supply.
the usual problem with these transformer type power supplies is a thermal fuse inside the windings it can often be looped out with spare taps on the transformer.
since it is knackered already - i will be happy to take a look at it for you.
the worst thing about these things is taking the case apart and reassembling the case afterwards.
thats no worries mate - you can purchase a step down transformer all over the place to make the power supply work.
of course you will need to know what you are doing electrically. as i said i reckon if your that stuck i could breathe some life into it as a last resort.
i think the sega megadrive is a 10v transformer so it probably rules it out.
as long as you buy a 12v 1amp unregulated supply you should find it works no problems, as these usually dish out at least 13.5 volts upto an amp.