What do I do when only the grey screen appears on my Mac desktop?

The dark gray Apple is loaded off your boot Drive. If you are not getting that, your Boot drive is in trouble.

Try Safe Mode: Hold down shift at Startup and wait five minutes while it does a Disk Utility (Repair disk), then invites you to login with your username and password, even if you normally auto login.

If no joy, Hold down Alt/Option key at Startup, wait a minute while it finds all potentially-bootable Volumes, choose Recovery_HD if available and use Disk Utility to (Repair Disk) manually.

update your profile to reflect mac model and OS more clearly.

You might want to search out for the OS X and iMac Communities.

Mac OS X Forum
https://discussions.apple.com/community/mac_os?view=discussions

The more backup sets you have the better. And some basic knowledge of system maintenance.

http://www.apple.com/support/macbasics/

Isolating Issues in Mac OS

http://support.apple.com/kb/TS1388

https://www.apple.com/support/osx/

https://www.apple.com/support/quickassist/

http://www.apple.com/support/mac101/help/

http://www.apple.com/support/mac101/tour/

Get Help with your Product

http://docs.info.apple.com/article.html?artnum=304725

Apple Mac App Store

https://discussions.apple.com/community/mac_app_store/using_mac_apple_store

How to Buy Mac OS X Mountain Lion/Lion

http://www.apple.com/osx/how-to-upgrade/

TimeMachine 101

https://support.apple.com/kb/HT1427

http://www.apple.com/support/timemachine

Mac OS X Community

https://discussions.apple.com/community/mac_os

Recovery Mode

http://support.apple.com/kb/HT4718

ExpressLane

https://expresslane.apple.com/

Startup Manager: How to select a startup volume

http://support.apple.com/kb/HT131

Startup Key combination: here is the old list:

http://support.apple.com/kb/HT1343

Startup Key combinations new list

Troubleshooting: My computer won't turn on

https://support.apple.com/kb/TS1367

How to Clone a Volume
Using Cloning as a Backup Strategy

See also Erasing a Drive, How and Why to Partition a Drive, RAID.

http://www.macupdate.com/app/mac/7032/carbon-copy-cloner

Using Cloning as a Backup Strategy

http://macperformanceguide.com/Mac-HowToClone.html

Mac OS X: Starting up in Safe Mode - http://docs.info.apple.com/article.html?artnum=107393

What is Safe Boot, Safe Mode? (Mac OS X) - http://support.apple.com/kb/HT1564

Isolating issues in Mac OS X

Creating a temporary user to isolate user-specific problems:

Isolating an issue by using another user account

Identifying resource hogs and other tips:

Using Activity Monitor to read System Memory and determine how much RAM is being used

Starting the computer in "safe mode":

Mac OS X: What is Safe Boot, Safe Mode?

To identify potential hardware problems:

Apple Hardware Test

General Mac maintenance:

How to install OS X on a new or faulty HD without Internet recovery

Corrupt and new disks might not have a working Recovery partition, but there are still ways to access one and reinstall OS X, if needed.

If you do not have current Backups, you should use this "near-death experience" to convince yourself to buy a large-ish External drive (two to three times the size of your data) and do at least Time Machine backups. USB-2 is too slow for daily data, but fine for backups, and the enclosures are cheap.