MacBook Pro can't boot: shows Apple logo then grey screen
Try to do a file system check via single user mode.


Reboot and immediately press Cmd+S
Wait for the command line and then type /sbin/fsck -fy
Have a tea. And a cookie.
Have a look in the output. If the HDD is failing you might see something like I/O Error. If you see something like ***** FILE SYSTEM WAS MODIFIED ***** then you can try to do it once more. If Volume X appears to be OK then you might be lucky.
Type reboot and let it boot.


More info on apple's website.

Good luck!