1987 F-150 ignition problem

Maybe you can help me out,I'm no mechanic. My '87 Ford F-150 has issues. A month ago I started it up and the starter kept engaging, I tried to turn it off, but it wouldn't shut down. I heard a pop, and it died. So I replaced the starter, and had no problems until today. Luckily I was able to disconnect the battery before the starter blew again. Now, I had already replaced the relay when I put the new starter in, so I don't think that is the problem. The ignition key tumbler was a little wore out, so I replaced that. But, even with the ignition shut off and the key removed, I reconnect the battery and the starter engages. I need some input here, any ideas?
The key isn't the electrical part of the ignition's switch so look further down column. Most were recalled in the 80s for screwing up and if solenoid is new then I really doubt that you got another bad one. If key fails to return to plain run there are issues with the rod to the switch or something screwey. Fords of the era had issues - most not exactly this but key would remove when NOT really in full OFF mode and drain batteries and some (like two) cause a fire.
Solenoid is the first thing the positive battery cable goes to. If in question replace that as it could do this too. You called it or whatever a "relay" and I'm thinking the actual solenoid,

T

PS: Large wire in, large gauge wire out. It's triggered with a little one you could just pull off, put back on with key in "run" position and truck should start if you add power to that small post then remove it and all should be ok to use till you need to start again,