Well, the prize goes (tenatively) to... Kingdav1954, for his suggestion about the loose connections / bad ground inside the rat's nest in the RCM box.
I checked all the grounding points on the chassis that I could identify, and and they all looked clean & correct. I opened the box which contains the RCM, took the RCM out, and checked the solder points per the sticky on that topic, just for good measure. They all looked fine.
Got back in the car and turned the key - still nothing from the starter, BUT now the accessories and dash stayed on even after turning the key to the Start position. Hmmm...
Got out and took RCM out of box again. Jiggled all connections and pressed them very firmly back into sockets.
Car started up without a hitch. Drove it home, shut it off, started it up again. It's like it never happened.
So now I'm a little worried that whatever was out-of-whack could wriggle out of place again at any moment, leaving me stranded somewhere. But if it does at least I (with patience and a little luck) have a fix. Thanks to everyone for their advice!
Two parting questions:
Do you think re-grounding the battery to the chassis with a DIY hack as Pizzaguy described would prevent this from happening again, even if whatever was loose in the RCM box were to go wrong again?
Also, does it make sense to replace the RCM just for good measure? Or is that unlikely to have been related to my issue, in your experience?
Thanks again for all your help! This site/community is amazing.
