This is an odd issue - I’ll be glad to assist.
I think there are two likely possibilities given what you’ve described. Either there’s an internal defect with the cable, or the HDMI port on the PS4 isn’t outputting sufficient power for the converter chip in the cable - or perhaps there’s some underlying PS4 DRM/content protection in place that doesn’t allow output via analog connection. (We haven’t had any customer feedback regarding using the cable with the PS4, so at this point we don’t know if it would be expected to work.)
I think the best approach will be to have a replacement cable pre-tested in our labs and sent to you, which should either resolve the issue, or confirm that there’s a underlying compatibility issue causing the green screen.
At your convenience, can you please email firstname.lastname@example.org with your Amazon Order ID number from the cable purchase as well as your preferred shipping address, and I’ll get things arranged for the replacement. Also, please put “Ticket 84327” in the subject line.