macbook stuck on grey screen

It would help us to know which computer model you have, which OS you're using, how much RAM, etc. You can have this info displayed on the bottom of every post by completing your system profile and filling in the information asked for. This will help in providing you with the proper and/or correct solutions.

If you don't have a backup of your files off the machine, try holding the Shift key down on a wired/built in keyboard and boot the computer (you can do a hard shutdown by pressing and holding the power button)

This will hopefully allow you to get into the machine in Safe Mode and backup your user file folders (Music, Pictures, Movies, Documents) to a external storage drive (not only TimeMachine!)

Most commonly used backup methods

If Safe Mode (Shift Key) doesn't work, then you can follow these directions to attempt to get your files off. However it's not necessary as the repair step shouldn't affect it.

Create a data recovery/undelete external boot drive

If you have a backup off the machine and or want to continue with the repair, do the #8 Reinstall Just Only OS X + Software Update procedure here and other Steps as required.

..Step by Step to fix your Mac

#8 will replace the OS X with a new copy overwriting the old one and removing anything installed in OS X itself from third party software makers.

Some programs might not function, you first need to find out if there is a update and compatible with your OS X verison before reinstalling them.

Run through the other Steps to make sure your machine is working as intended.