Control, Option, and Shift keys (on left side) do nothing.

The bad Magsafe charger explains why the old board stopped charging, too bad, it was a very expensive charger in the end although the charging circuit could be fixed by a component level repair, that comes cheaper than a replacement. However, I never experienced a keyboard going bad as a side issue of a faulty charging circuit, the problem must be somewhere else. Shift, control, option and power buttons have a double function in a keyboard as they’re connected to the SMC for reset and other system toggles. Unless you had a spill, big or small in the past, or keyboard has gone bad out of the blue, there might be a board SMC issue. I’d try if a SMC reset works as a first thing. As a second step I’d try again your old board to double check there isn’t a keyboard failure. I know it’s a headache but a KB replacement on a retina is a big job and a topcase replacement pretty expensive..investing a couple hours work in troubleshooting seems to me the best option.