Chosen Solution
My PS4 boots up with no sound and the video flickers on the TV in my bedroom. I moved the PS4 into the living room and it boots up totally fine. Same thing happened at a friends house; one TV works and one TV doesn’t work. I’ve tried different HDMI cords and outlets and nothing works.
That is a symptom of the HDMI encoder IC chip going bad. It will require someone with micro-soldering experience to replace that chip. A local reputable repair shop can test the console, confirm that whether or not the HDMI chip is at fault.