Well, if you cannot even see the OpenFirmware prompt, that is quite bad news.

You could try to boot MorphOS from CD (by pressing C). This way, you would know if MorphOS works with default settings at least.

Still, as I wrote before, this monitor is generally a bad fit for a Mac Mini G4, which barely manages FullHD at normal refresh rates.

It is also possible that whatever DVI-to-HDMI adapter you use might be to blame.