I am connected via DVI to an ASUS PA278QV. There is an initial gray screen, but the video goes dark, the instant the CD starts spinning up. The mouse and keyboard seem to be alive.

A mini is incapable of producing output above FullHD. MorphOS is trying to match the resolution of your 2k display and fails (we've corrected this for 3.20).

Try holding the CTRL button when you boot, this will force a lower resolution screen mode. From there, go to Settings / Screens and make sure to pick a mode that's no more than 1920x1080, ideally 16bit color since the mini lacks the required graphics ram to comfortably go higher.