Q: Blue/Gray Screen Stuck on Startup: Best Actions In Safe Boot?

See OS X Mountain Lion- If you see a blue screen at startup. I suggest the last recommendation - reinstall OS X:

Reinstalling Lion/Mountain Lion Without Erasing the Drive

Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.

When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.

Reinstall Lion/Mountain Lion: Select Reinstall Lion/Mountain Lion and click on the Continue button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

No, it just replaces all the OS X system files with those from the installer. It does this by simply running through a standard installation so that only system files are replaced. User files are left untouched. This is essentially the same as a system upgrade.