Hi all,
I wanted to add my experience to this thread, in case it can be of use to anyone.
On Monday morning I tried to install the 10.11.5 update. The instillation seemed to go fine until the reboot, when it got stuck. After giving it about six hours, in case it needed all that time, I tried to reboot in safe mode but could not. I then rebooted into disk utility and ran "first aid" on both drives. Again the computer got stuck on reboot. I tried to reset PRAM, but again on restart it got stuck. So I restarted again into disk utility and this time reinstalled OS X (which took a few hours). Again it seemed to progress normally until the reboot, when it got stuck. Third time, tried to restore from time machine backup, and again progressed normally until the reboot, when it got stuck (another four hours... I actually let it try to reboot overnight so it spun on the grey screen with the apple logo for seven hours).
Having spoken to Apple Support and exhausted all options I took it in to an Apple Care centre on Tuesday morning where they wiped it and installed Yosemite. I then upgraded to El Capitan 10.11.5 and everything was looking good. THEN I MADE THE ERROR OF TRYING TO RESTORE FROM TIME MACHINE BACK UP (while on the phone with Apple Support, so I definitely followed the correct steps). Don't do this! Because after all the backup data transferred from my external time machine harddrive to my Mac harddrive it AGAIN got stuck at that grey screen during reboot. Again northing worked to get the computer to turn on normally, it just always got stuck on that grey screen during reboot.
On Wednesday morning I again had to take it back to the Apple Care Center and they again wiped it and installed Yosemite. I again upgraded to El Capitan 10.11.5 and have now just copy-pasted files from my time machine onto my harddrive. I freshly reinstalled all software, etc. Everything is fine now (fingers crossed it stays that way.) Just wasted three whole days. I still don't know what caused the initial problem but I guess El Capitan 10.11.5 and something on my computer, some software or setting, just did not get along.
I could have tried getting El Capitan 10.11.4 and restoring from time machine but I was exhausted and desperate to get back to work, and didn't want to risk another crash. Plus now my computer is fresh and not running any crap software that caused trouble during the upgrade.
Good luck all. And Apple, please try to figure out what the heck is going on. Losing three days of work is quite problematic. Plus my three year extended warranty expired May 19, 2016 and so when all this went down on May 23, 2016 I was juuuuuust out of warranty and had to pay for the reset. And I had to pay to re-install some key software. So, yeah, this sucked.
Best wishes,
Kerry
Computer info:
MacBook Air (13-inch, Mid 2011)
Processor 1.7 GHz Intel Core i5
Memory 4 GB 1333 MHz DDR3