Yeah, it would matter. If you are missing the ground, then you would not get the voltage to the RAM that is needed to hold the settings. Actually, I don't think that battery (-) is connected in the right place.

After all that battery damage repair, I believe NVRAM is always the way to go, especially if you can solder. https://www.pinitech.com/products/6264_nvram.php

Yes, it should boot up fine without battery. What are the state of the 3 red LEDs on the board?

Yes. That is why all the copper area is showing. Normally those areas would be covered with green masking, just like the rest of the board.

Then unplug all the ribbon cables. Does it boot now? A good boot is the middle LED would be blinking fast and the top LED will turn off. If not, press on all the socketed IC chips.

If it boots without all the ribbon cables connected, then reseat all the ribbon cable connections starting at the CPU board, making sure that the ribbon cables are not plugged in one row off.

Yes. That one will work. It is guaranteed to be 2%, which is better than the 5% mentioned in the manual.

So it measures open?