Again, has anyone found specific issues with the Cruz board which are repairable?
Not for your problem. Also the normal method of repair is replacing the entire component, which is normally constructed only by machines and intended to be serviced by replacement. This is the nature of advanced microelectronic technology, chips etc. These are computer systems like a PC or smartphone, with a cleaning peripheral.
If the LCD remained lit, is it possible that it is not the problem?
No. A number of LCD modules have had to be replaced.
What actually determines the text on the LCD? Is it the LCD or the motherboard?
Both. This is a complex digital electronics function. The particular design is proprietary and not disclosed.
Usually blank LCD's are defects in the LCD but there is no way to tell without first replacing it, then see if the system board needs replacement. And this applies only to the one problem of defective display.
I understand the concerns about the $$$ of the items, but I would obviously look for something used reasonable on-line.
There are a couple of used Samsung Powerbots online in the U.S. if you are there, and they haven't sold already. The product is only a year old and is normally more expensive than Neato. These units employ a more advanced guidance system with solid state cameras instead of lidar with moving parts which wear out. Ten years of progress in electronics since Neato started makes a difference. The latest most expensive Roomba uses this tech as well. Nothing is perfect in this category though, and every brand has its fans. Check how long and hard the powerbots were used as the battery is large and more expensive than others -- but may last longer. The special advantage of this robot is covering large spaces.
It's all a matter of what deal you find and your personal tastes and application. There are many reviews of all these products.
This topic should be pursued in a separate thread, not being the specific component problem identified in this thread.