Firstly I would like remind you about grounding.
Canned Grounding Rant-
shut down system and remove side panel. with the power cable plugged into the PSU touch a bare unpainted metal area of the case. (my favorite spot is an unpainted screw securing the PSU) once you have grounded yourself you can unplug the computers power cable from the PSU and can touch the system.
if you move your feet, or shuffle in your chair, plug in the cord, reground yourself and unplug again.
end canned rant-
I would suggest clearing the BIOS/UEFI by removing the battery (looks like a silver coin) while the PSU is unplugged from the motherboard for five minutes or so.
if that does nothing to fix it I suggest removing the rx580 and trying the iGPU in the intel CPU. removing the 580 should enable the internal GPU. if the iGPU works the cable is good, (still suspect) and the problem has to be the rx 580.
is there a speaker connected to the front panel connector on the motherboard?
http://www.tomshardware.com/forum/261145-31-perform-steps-posting-post-boot-video-problems
step 17
canned diagnostic speaker rant
The diagnostic speaker is the motherboards main diag feedback device.
the motherboard may be telling you where the problem is.
my speakers have this plug
http://images.crutchfieldonline.com/graphics/infolib/homelib/hSpeakerSpringClip.jpg
I use lamp wire but any stranded wire will do. literally any stranded wires. strip one end like so
http://www.antiquelampco.com/Shades/CordColors.jpg
attach the stripped end into the speaker spring clips on the speaker.
the other end of the wire should be trimmed like so the semi strip
https://wesbellwireandcable.com/images/cutwire.png
by doing a semi strip the wire case is now the socket.
plug one wire to the first pin, and the second onto the fourth pin.
power on the system and listen for beeps
end canned rant