Thank you for the reply Sylvia,
You are right, it is a power issue of some sort.
I have done some more testing, both with two DH77KC systems, but also with 2 older DG43NB systems.
What I have found is that there is a difference on how the DH77 and the DG43 systems handle power to USB devices, it is not a single DH77 system that has this issue.
When I boot up the two DH77 systems, the system connected to KVM port 1 boots, but I get no picture, but i get a picture on the system connected to port 2.
If I switch the two systems, the same thing happens, this is consistent.
If I remove the mouse or the keyboard from the KVM switch, or change keyboard or mouse brand/model, the DH77 behaves differently.
If I remove the mouse or the keyboard both systems boots up with picture and everything, the same thing happens with different keyboard/mouse combinations, but I have also experienced that it seems to work, but in reality the functionality of both devices is unstable, as if it is loosing connection to the system.
None of this happens with the DG43 systems, they work with every combination I have tried.
To me it seems that the DH77 either delivers less power to the USB ports or it handels the way it delivers power to the USB ports differently.