I have a Mac Mini 2012 and since installing OS X El Capitan (I am now on MacOS Sierra) with no other noticed changes my system I have had this rather annoying problem.

I can power on the Mac, it boots up quickly, as expected I log in and everything is fine. It goes to sleep, it wakes, it works fine.

Now... I either shutdown or restart and it never successfully boots again after the shutdown. It chimes, and the power light comes on but there is no signal to the display (Display Port or HDMI - have tried two different monitors). I have no option but to force it off (I have waited as much as a whole day and it never progresses), then when I power it back on I either get a password recovery screen OR it boots fine.

Any ideas on what on earth this could be?

Have reset start up disk permissions, I have decrypted my drive with FileVault, re-enabled FileVault to no avail.

Look forward to hearing any suggestions.