Yeah, it was your family's old copy.
The console works so long as it gets a good connection with the cart. Previously I would just reinsert it until it would play along. In taking it apart I saw that the problem is perhaps some trace damage where the 72 pin connector touches the main circuit board, and even though the connector has been fixed, it still doesn't work better.

Possibly fixable if I can find the right thing that I don't even know the name of (pen to draw circuitry traces) with some hard effort on a microscopic line. Crap.
The VCR style "pop-in, push down" has everything to do with Nintendo trying to make the NES seem attractive, familiar, but distant from Atari to U.S. customers. The Famicom looks like an Atari where you plug a game in on top, and after the video game crash of '84 that appearance came in doubt. The flat top brought with it the unintended side-effect of people putting drinks on top of it, which would often spill, and accounted for a large number of service calls. SNES and N64 having weirdly non-flat tops were attempts to keep cans and glasses of soda off consoles. The 72 pin connector itself flexes to let the cart up/down, and that movement stresses the metal and wears out it's level of spring. The connector doesn't hold the cart any more or less in the up or down position when new, but wear pushes the connector pins down and sometimes one or more is too far down to touch the cart unless the cart's pushed into the down position (and sometimes not even then).
"Yes a working NES would be ideal but it doesn't, right?"
Yeah, keep picking on me.
