my desktop turns on but nothing is displayed on the screen. It's just grey.

Your data is on your Time Machine (or bootable clone) backup. If you have not been backing up you are about to learn a painful lesson on why backing up is NOT something you "should" do, backup is imperative and simple. Back up your Mac with Time Machine & OWC Mercury Elite Pro

Your options assuming the issue a hardware problem to get your data:

• Remove the drive from the computer and put it in an enclosure and move the data to another computer.
• If you have another Mac available use Target Disk Mode
• Hire a data recovery service.

Welcome to the Apple Support Communities.

Have you followed the steps here: If your Mac starts up to a blank screen - Apple Support?

Jack

What model, year and OS are you running.