Good morning,
Someone I know had a similar issue with a MacBook Air. The individual had done an update to the OS and once the Air went through the start up and arrived at the log-in screen fine. The issue started once the individual input their log in password. The log in screen would change into a white screen indicating the individual was about to enter their account but came to the sad conclusion they would stay on this white screen of death indefinitely.
The individual asked for my help knowing I have been an Apple user for some time. So with the help of the internet and my experience I went through the usual steps everyone on the net would guide anyone. I started by doing a "Disk Verify"and then a "Disk Repair"just to make sure everything was good; even tough I have been told since MacBook Airs use flash there is no need. The following step was to reset the PRAM. After that I went on and restarted the MacBook Air and ran into the same problem once more. The boot logo comes on and then I got the log in screen. Once I entered the individuals credentials I inevitably got the "white screen of death". My last try would be to go into a "Safe Mode" by restarting the MacBook Air while holding down the "Shift key". Wala, I was able to access the individual's account so they can save any information needed before I try an erase and install. Hopefully once they have extracted whatever information they need the erase and install will fix the issue.
I hope my experience with the "white screen of Death"helps anyone still trying to save there personal information which they thought might be lost.