There are about a dozen questions similar, but all of them get further along in the startup than I do. Purchased a used MacBook Pro 2012 (December 2011). Seller (whom I trust) said that it wouldn't start and she was told a procedure that included removing the battery. She was scared of that and took it to a genius bar, where it was "fixed" for free. Must have been something simple if they did it out front while she waited.
It worked fine for her and she installed El Cap but stopped before the "assign admin password." I did that so that I could log in and verify WiFi worked and no obvious issues. Bought it and it worked for me for a few days.
But now, press power, screen lights up but goes dark within a half-second. Sleep light on but not pulsing. Keyboard not lit. Hold power down and can hear the turn off click (and see the sleep light go out). Resetting SMC did not help. Battery is fully charged according to the LEDs.
I'm guessing that it's the same problem she had, but maybe not.