This white (or gray) screen means that your mac OS or OS X can’t start because of problems with the system’s hardware or software.
If your Mac fails to start-up regularly, try these few things to troubleshoot your problem(s).
If you do not have i Tunes on your computer, download and install the software via the link in the Resources. It also notes, however, that once the process is complete, you'll have the option to restore your contacts, calendars, text messages and other settings. You will have the option to set it up as a new phone or restore it from a backup. Click "Continue" and a progress bar indicates that i Tunes is restoring from backup.
If your Mac doesn’t have 10 GB free, move some of your largest files to another drive (either internal or external–JUST NOT another folder on your Macintosh HD.
Look for video files and image files as these tend to be your largest and are easy to move.
If at all possible, use the Apple branded keyboard and mouse that shipped with your Mac.. Now Turn on your computer by pressing the power key while holding down the Shift key.
Re-building this Launch Database often resolves your Mac getting stuck on the white screen. When you see the Apple logo, release the Shift key.
You may wait for the message to disappear or click "OK." After the phone shows in i Tunes, the software will reinstall your phone's apps, if you have any, and music.
Once the process is complete, the LCD-type display window in i Tunes will state "i Phone sync is complete.
After your Mac fully starts, restart your computer normally without holding any keys/buttons during startup. After dumping the trash, open a Finder info window on your hard drive (default name is Macintosh HD unless you gave it a different name.
Verify that this hard drive has AT LEAST 10 GB of available space.
Resetting PRAM or NVRAM might just fix your boot failure.
PRAM (parameter random-access memory) or NVRAM (non-volatile random-access memory) is a small amount of your computer’s memory that stores certain settings in a location that mac OS can access.
Then you should see a Mac OS X Utilities or Mac OS Utility window.