You are off to a good start. With the home pin everything starts at the power supply and you are on track checking the voltages.
You say the game is booting? and you can launch a ball? Is everything working otherwise except for the switch problems you describe?

Your problems appear to be with the display and switches. It's been a while but at least you have the schematic and support manual.
Read through it and try running the self tests.

I glanced over the matrix diagram and it appears all the switches you are having problems with are on the same row of the matrix. That's an important clue and could indicate a bad connection to the mpu board or a faulty driver chip.

I would start by trouble shooting the simplest a loose wire or bad connection at the board. If you have the same schematic I have the matrix is shown in figure 2A. Mx0 wire appears to be common to all the switches that do not work. Since the problem is split between the tilt and the playfield I'm guessing if it's a wiring issue it's gong to be with the MPU connection.

Bally home pins are indeed excellent starter games to learn on. Overall not much value but in working condition a good starter pin for a young family.