After installing Maverick my computer, when restarted, only a gray screen appeared. My computer won't work at all...what happened?

Question

After installing Maverick my computer shut down and when it restarted I couldn't get to the home screen. The monitor was grey with some dark grey shapes, it sounded like it was constantly running a program. My computer is sick!! HELP

Answer 1

Take each of these steps that you haven't already tried. Stop when the problem is resolved.
Step 1
The first step in dealing with a startup failure is to secure the data. If you want to preserve the contents of the startup drive, and you don't already have at least one current backup, you must try to back up now, before you do anything else. It may or may not be possible. If you don't care about the data that has changed since the last backup, you can skip this step.   
There are several ways to back up a Mac that is unable to start. You need an external hard drive to hold the backup data.
     a. Start up from the Recovery partition, or from a local Time Machine backup volume (option key at startup.) When the OS X Utilities screen appears, launch Disk Utility and follow the instructions in this support article, under “Instructions for backing up to an external hard disk via Disk Utility.”
b. If you have access to a working Mac, and both it and the non-working Mac have FireWire or Thunderbolt ports, start the non-working Mac in target disk mode. Use the working Mac to copy the data to another drive. This technique won't work with USB, Ethernet, Wi-Fi, or Bluetooth.
c. If the internal drive of the non-working Mac is user-replaceable, remove it and mount it in an external enclosure or drive dock. Use another Mac to copy the data.
Step 2
If the startup process stops at a blank gray screen with no Apple logo or spinning "daisy wheel," then the startup volume may be full. If you had previously seen warnings of low disk space, this is almost certainly the case. You might be able to start up in safe mode even though you can't start up normally. Otherwise, start up from an external drive, or else use either of the techniques in Steps 1b and 1c to mount the internal drive and delete some files. According to Apple documentation, you need at least 9 GB of available space on the startup volume (as shown in the Finder Info window) for normal operation.
Step 3
Sometimes a startup failure can be resolved by resetting the NVRAM.
Step 4
If you use a wireless keyboard, trackpad, or mouse, replace or recharge the batteries. The battery level shown in the Bluetooth menu item may not be accurate.
Step 5
If there's a built-in optical drive, a disc may be stuck in it. Follow these instructions to eject it.
Step 6
Press and hold the power button until the power shuts off. Disconnect all wired peripherals except those needed to start up, and remove all aftermarket expansion cards. Use a different keyboard and/or mouse, if those devices are wired. If you can start up now, one of the devices you disconnected, or a combination of them, is causing the problem. Finding out which one is a process of elimination.
Step 7
If you've started from an external storage device, make sure that the internal startup volume is selected in the Startup Disk pane of System Preferences.
Start up in safe mode. Note: If FileVault is enabled, or if a firmware password is set, or if the startup volume is a Fusion Drive or a software RAID, you can’t do this. Post for further instructions.
Safe mode is much slower to start and run than normal, and some things won’t work at all, including wireless networking on certain Macs.
The login screen appears even if you usually log in automatically. You must know the login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
When you start up in safe mode, it's normal to see a dark gray progress bar on a light gray background. If the progress bar gets stuck for more than a few minutes, or if the system shuts down automatically while the progress bar is displayed, the startup volume is corrupt and the drive is probably malfunctioning. In that case, go to Step 10. If you ever have another problem with the drive, replace it immediately.
If you can start and log in in safe mode, empty the Trash, and then open the Finder Info window on the startup volume ("Macintosh HD," unless you gave it a different name.) Check that you have at least 9 GB of available space, as shown in the window. If you don't, copy as many files as necessary to another volume (not another folder on the same volume) and delete the originals. Deletion isn't complete until you empty the Trash again. Do this until the available space is more than 9 GB. Then restart as usual (i.e., not in safe mode.)
If the startup process hangs again, the problem is likely caused by a third-party system modification that you installed. Post for further instructions.
Step 8
Launch Disk Utility in Recovery mode (see Step 1.) Select the startup volume, then run Repair Disk. If any problems are found, repeat until clear. If Disk Utility reports that the volume can't be repaired, the drive has malfunctioned and should be replaced. You might choose to tolerate one such malfunction in the life of the drive. In that case, erase the volume and restore from a backup. If the same thing ever happens again, replace the drive immediately.
This is one of the rare situations in which you should also run Repair Permissions, ignoring the false warnings it may produce. Look for the line "Permissions repair complete" at the end of the output. Then restart as usual.
Step 9
Reinstall the OS. If the Mac was upgraded from an older version of OS X, you’ll need the Apple ID and password you used to upgrade.
Step 10
Do as in Step 9, but this time erase the startup volume in Disk Utility before installing. The system should automatically restart into the Setup Assistant. Follow the prompts to transfer the data from a Time Machine or other backup.
Step 11
This step applies only to models that have a logic-board ("PRAM") battery: all Mac Pro's and some others (not current models.) Both desktop and portable Macs used to have such a battery. The logic-board battery, if there is one, is separate from the main battery of a portable. A dead logic-board battery can cause a startup failure. Typically the failure will be preceded by loss of the settings for the startup disk and system clock. See the user manual for replacement instructions. You may have to take the machine to a service provider to have the battery replaced.
Step 12
If you get this far, you're probably dealing with a hardware fault. Make a "Genius" appointment at an Apple Store, or go to another authorized service provider.