PS4 Beeping and ejecting disc (or in my case not taking a disc and beeping intermittently all day) – solution:
After suffering this for what seems like an age (with unsuccessful attempts to resolve), and with the pending delivery of Wipeout Omega collection I though again I would trawl the internet for a solution.
Surprisingly I found one that resolved it immediately, simply by turning the manual disc eject screw a few times in the opposite direction for manual ejection (i.e. clockwise). Follow this support article from Sony:
https://support.us.playstation.com/articles/en_US/KC_Article/PS4-Manually-Eject-a-Stuck-Disc/
More information can be found on the Playstation community here:
Update: It would appear through convection that the shiny removable cover on the PS4 naturally generates static which interferes with the touch buttons. I have un-clipped this, though still leaving it in place; this has finally cured what appears to be a deisgn flaw!