I have an HP Omni Pro 110 AIO, setting here and doing the exact same thing.
I can hear what seems to be boot noises but no screen at all. No HP Logo, no BIOS Post information, no nothing.
So I assume it is likely the screen itself and with no external monitor port on the thing, I can't test.
One of these days when I get some extra time and feel particularly ambitious, I'll probably tear it down and see what I can see (further than removing the stand and the three back panels).
I'm not even sure how the screen interfaces with the motherboard and the power supply, I'm assuming at this point that it is something similar to a laptop screen with its' own discreet power converter and digitizer.
I can't even find a place selling replacement screens or other parts for these things.
So..... sorry I couldn't help but if you happen to find any information relative to the problem please post back and let me know.