Swapping logic boards looks cheaper and less wasteful than buying new computers. This is relevant in 2018 because macOS Mojave relies on particular graphics processors for its “Metal” graphics language (as they dropped support for OpenGL). Us oldies must search for post-2012 graphics boards.
There will be no answer. Apple Mac Minis go blank after the screen saver operates. Then they will not recover. I know neither cause nor solution. I suspect that there is a hardware or firmware fault, as altering software (ie any settings at all) seems to have no effect. In any case, Apple will not acknowledge the issue. I work around this by turning the Mac Mini off and then back on again. richard horobin Canberra, Australia 2016