I will assume that you waited long enough for the start-up after the updates? You usually get a "double-restart" and it can take a bit long.
Assuming that is not the case . . . and you have failed to get it to restart . . . make sure your computer is not "searching" for your hard drive--when you are in
Disk Utility go to System Preferences > Start-Up Disk and see if your OS is chosen.
If not . . . choose it.
See if that works.
If that does not work then it may very well be that something is FUBAR'd with your OS. A Guru may correct me, but that permission repair is taking
hours suggests there is a problem.
DI may not necessarily diagnose/fix a FUBAR. I know this having done the very thing!
Okay . . . now comes the question ALL who seeketh computer wisdom hat[eth--Ed.]
Did you back up all your data?
If the answer is "yes" than . . . congratulations! You can simply start over while watching the repeat of the Celtics crushing the Atlanta Hawks--erase and install. Install all of your software, then try downloading the "Combo-update" and install that--Gurus HERE say it is better than trying to update an existing System--transfer your account--the OS will ask you if you want to transfer your account.
If the answer is "no" . . . well . . . try to see if you
can back up your data--see your files, copy them under
Disk Utility. I have gotten away with this.
If time is not a factor, consider purchasing
Disk Warrior which is a great program for fixing FUBAR'd volumes or at least taking an "image" of your data that you CAN pull off before you start over.
If it is, consider
Archive and Install. This basically replaces your OS and leaves "you" intact. It often corrects the problem, but if part of the cause of the FUBAR has to do with "you" it may not. So you may consider doing that to see if you can start up your computer . . . get your data . . . save it . . . then consider a clean install.
Now, if you have the time, external HDs are relatively cheap now. I would recommend getting one. This will be where you "put" your data conveniently. You can even--since your computer boots on the installation disk--install OS X on the Ex-HD--make sure it is "journaled." So if all else fails, you can boot your computer off of that as you try to save data.
--J.D.
