Mac mini 2018 does not start up/monitor issue
I just want to report that, after having lots of troubles with starting my new Mac Mini, I defined a procedure that makes it start up every time: I disconnect everything at the back except the HDMI monitor, Ethernet network and USB keyboard (with mouse). It starts up every time. Then, I can connect the rest (second 22' 2K monitor via VGA adapter to USB C, USB printer and external HDD USB disk)
As it is not very convenient (in order to limit wearing off the connectors), I only do this about once a week or when I suspect the Mac needs a reboot.
(Monitor: Samsung S22F350 (2k HDMI); Mac mini (2018) 3 GHz Intel Core i5, 8 GB DDR4, Intel UHD Graphics 630, upgraded to 500 GB SSD; Mojave 10.14.4)
Hope it helps out there...
Mac mini, macOS 10.14