I may know a fix. Look at the C404 chip on the video pcb. There are three ram chips near that custom which is the palette ram. Replace all three of them first. They are 32k x8 SRAM (SOJ2; originally NKK N341256. If replacing the ram doesn't work, then it might be a bad C404 or some pins need to be resoldered.
This issue is more common on Namco System 23 pcbs as that uses a C404 as well (hint: replace the fan if the pcbs get dusty). Both my Motocross Go pcbs were dusty and one fan didn't spin so I cleaned both pcbs and replaced the fans. I was pretty lucky both pcbs didn't give me a C404 error (same for a twin Time Crisis 2 I restored).
It should. Decided to look at a Namco System Super 22 video pcb (since Cyber Cycles is System Super 22 as opposed to regular System 22). The ram chips match the one you linked. There are more of these ram chips at different locations if you wish to replace them eventually.
As a matter of fact, yes. To find out which board is defective, you will have to do some board swapping with your friend's Time Crisis pcb set. The issue itself looks like bad ram on whichever board is defective.