MGB: Engine Run ON with a twist

I have a good one for you. I purchased a 78 MGB a few months back. It never shut off!! The previous owner had installed a kill switch to shut the car off with. Heres the twist. I bought a used radio from a 79 MGB, and installed it. The radio only worked if I was 'driving' over 25 mph. Just reving the engine didn't help. I checked the wiring on the radio and noticed it wasn't grounded. I grounded the radio, and NOW the car shuts off with the key everytime, as long as the radio and lights are off before I turn off the ignition.

Any thoughts?

Too Totally Strange!!
My initial impression is you have some very messed up wiring. I would start by going over the entire wiring harness with special attention to the ground connections. Also, looking for shorts, any "rigging" done by PO's or mechanics, and finally, trying to isolate where the problem is by disconnecting parts of the harness. You'll need to do it anyway to clean up the connectios, so why not also see if it helps isolate the problem. It sounds daunting, but something may "jump out at you" & then you can tell us "here's what caused it."
Good Luck!!

ive seen a bad ignition relay or one getting poor voltage do some really weird things try switching them out one by one(only two) and see what happends...i always keep two of them in my glove box just in case

I have been thinking maybe the ignition isn't grounded properly and is using the radio ground?
Also, is there supposed to be a ground wire from the engine to the car frame? I haven't found one or where one would go yet.
I did find a fried wire from the alternator to the starter. It was the smaller of the 2, and replacing it allows the battery to charge.
It makes me think that maybe the battery had shorted out against the body at some time in the cars past.

Your ground will be at the rear tranny mount. I have seen ignition relays cause this problem by keeping the alternator intergized thus feeding current to the coil which would let the car run with the switch off. You said a small wire was fried at the alternator. Can you tell what color it was. If it was or is brown and yellow,that is the entergizing wire. There may be a problem with the way it's hooked up,or related problem with why it fried in the first place.

My guess is that you have the switched (green) circuit shorted to the unswitched (brown) circuit when the lights are on. The radio should be powered off of the switched power anyway, so shouldn't work when the key is off. Actually, the only things I can think of that should be working when the key is off is the lights, interior light, brake lights, flashers and clock. If you have a voltmeter, check to see if you have voltage on the green wire at the fuse block when the key is off and everything else (radio, wipers, turn signals, etc.) is off. If not, that's good! Then start turing things on one at a time and see which one powers up the green circuit (with the key still off.) Once you find the culprit, check where it's powered from, and make sure it's ground connection is solidly grounded. Ground problems can cause all kinds of weird things to happen, so just be thorough, and use the wiring diagram in the manual to help. You DO have a manual, don't you? If not, the Bentley's is a very good one. I like it a lot better than the Haynes, but I have 'em both, because neither is very expensive and can save you a TON of time. Good luck and keep us posted.

The reason the car won't shut off is... the alternator is feeding back voltage through the ignition switch. There is a method to put a one way diode in the ignition system to remedy the problem, but most people opt to just replace the alternator. Good luck!