Upgrade to 10.10.4 does not complete, ask to restart endlessly
This should be easy to resolve.


Power down and boot into Recovery HD (Command R) or safe boot (shift)
Once you know the OS can boot itself - check for free space. Clean up cache or temporary files or delete large databases that you have backed up (Outlook email, Photo databases, Music Libraries) to get 20 GB of free space.
Run Disk Utility to ensure the disk structure doesn't need repair
Download the combo updater from https://support.apple.com/kb/DL1820?viewlocale=en_US&amp;locale=en_US
Run the update by hand and when the installer is running, open the log to watch for errors (Command L and then Command 3) if you desire or can see the log.