Hello,
Try different ports (hdmi, dvp etc..)
Also, check you monitor settings and see if its set to automatically detects the a/v from the ports!
b. update mobo bios (first thing you do when you build an new rig)
c. PSU needs lots of juice for that card to work in combination with an power hungry cpu !!
d. Did you connected both 2x 6pin connectors from you psu to your GPU ?
And finaly,do an bios reset !
I have the same Gpu RX580 8GB , and i had NO POST at ALL at first untill i checked that list ↑ up there (and a few other things i have forgot!)
EDIT: Most common things of no signal is that the Resolution is too HIGH !!
Start in Safe mode to see if you get AV back! In safe mode every healthy/working monitor should accept the resolution ..
Good luck
cheers,
TD