I'd guess you have a bad chip for the settings memory issue. Do you have power at the chip? If it comes to replacing it, consider putting an NVRAM kit in.

The sound issue might be the PIA on the sound board or maybe the amp is dead. See if you have an AMI branded PIA - they are notoriously bad. Do you get an audio thump when switching on? If not, consider the amp or speaker.

For the lights, if you have other GI I'd be thinking connectors, maybe bad sockets.

The audio thump indicates you're getting power on the sound board and the amp is working. The advice on checking for Scanbe sockets is good. Like the AMI PIA chips, they are notoriously bad. Did you check the PIA brand?

If you have a logic probe or a scope, you could check both the CPU and PIA lines for activity.

Those switches go through 2J13 on the driver board if I'm not mistaken. I think they're listed as the Special Switches and I believe they go direct to the CPU. I assume you pulled the driver and CPU boards to swap the battery holder. If so, I'd check the following things: 2J13 connector and header and the 40 pin interconnect. Look for cracked solder joints on both sides and you could lightly burnish the pins to clean them up a bit. I'd suspect the 40 pin first, especially if it hasn't been rebuilt. Those boards flex a lot when being handled and they're often old and worn out. That's typically one of the first bulletproofing steps recommended.