LG 49UH6100 set, and like many, the first time I hooked up my Pro I had the same issue.....black screen, and only audio. Setting the PS4 to safe mode and taking HDCP off of auto and changing to 1.4, allowed me to boot in and finish setup.
Once in, I disabled HDCP in the PS4 settings, and I was able to play games in 4K, but HDR showed as 'not supported'.
With all that said, if I'm in PS4 and then go into my tv settings and turn on Ultra HD setting, the tv resets, and then my Pro is in 4K / HDR mode.
The trick is....if I DONT turn that Ultra HD setting off in my tv before I put my PS4 in sleep mode, the next time I turn it on I get the black screen bs and have to do it all over again. Pain in the ass that we shouldn't have to do, but its a workaround for now.
I called both LG and Sony and both are getting bombarded about it. LG says their engineers are working with Sony on a fix, and Sony says their engineers are working hard on it too as a top priority. So my guess is a PS4 firmware update soon to address this since it's happening on many models, not just LG.
But damn...when it's working, the picture on this set in 4K / HDR is GORGEOUS!!!!