I have had the same issues, and the solution of changing the cable (to mini displayport-display port) and not using the Apple connector works for me.
I have installed El Capitan in MacBook Air early 2015. My external monitor is Dell P2314H. After the installation, I tried to connected them via mini display port, Apple miniDP to DVI/HDMI/DP connector, and Dell's display port. MacBook Air no longer detected the monitor, and the monitor didn't register any video input from the computer. Tried resetting PRAM, SMC, unplugged and replugged the monitor's power cord, bypassing user log-in, all to no avail.
I tried to connect via another brand's miniDP to VGA connector, and it worked. I tried to connect my MacBook Air to my LG HDTV using the same Apple connector via HDMI, it worked. I figure out the culprit must be somewhere between Apple's mini displayport and Dell's displayport. I bought a cheap miniDP-DP cable locally (I live in Jakarta, Indonesia), reconnected the two, and it worked.
I have re-activated user log-in in MacBook Air, and it still works.
I hope this helps.