[RESOLVED] (it was the CPU)
Thanks to all for the input, I solved this by Occam's razor logic, and going by what a ThinkPad expert had told me, elsewhere (and what sounded counter-intuitive to me) - "Try the CPU first" - yep, it went pop like a blown light bulb; can you Adam and Eve it!
Got a ThinkPad L540, had it running for 9 months. The other day as I was using it, the screen froze and I held down the power to restart it... and BLACK SCREEN!
Have checked/tested:
~ LVDS (video ribbon cable to LCD) is fine
~ RAM modules are fine (have also tested with OTHER "known good" RAM from my main laptop)
It turns on, and if I remove RAM altogether, I get the (expected) 1-3-3-1 beep sequence which indicates "Hey! What's up? NO RAM?" etc. So it is doing SOME portion of the "POST" ("Power On Self-Test") sequence.
i5-4210m is the CPU, have ordered a spare one from eBay.
Any help (apart from "bake the motherboard in the oven to reflow" type comments) would be most graciously appreciated, thanks!