Q: Hello, When I start my Macbook Pro ´13 2013, the grey screen with the apple appears and loads but then it "falls asleep" and when i press a key the mac wakes up but there is a black screen with the cursor. I have researched a lot but cant find a solution.

Mac OS X- Gray screen appears during startup.

MacBook Pro (15-inch, Mid 2010)- Intermittent black screen or loss of video

You may need to reinstall OS X. In any event I suggest you backup your files just in case. Better safe than sorry.

Not unless you have another Mac you connect to in order to use Target Disk Mode to transfer the data from the other drive assuming it is accessible.

If you don't wish to go the backup route, then what you can do is try an OS X reinstall that does not erase the drive. Frequently, this fixes the problem.

Reinstall Lion, Mountain Lion, or Mavericks without erasing drive

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair

When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported then click on the Repair Permissions button. When the process is completed, then quit DU and return to the main menu.

Reinstall Mountain Lion or Mavericks

OS X Mavericks- Reinstall OS X

OS X Mountain Lion- Reinstall OS X

OS X Lion- Reinstall Mac OS X

     Note: You will need an active Internet connection. I suggest using Ethernet

                 if possible because it is three times faster than wireless.

Blank (lighted, but black) screen with cursor at bootup

have tried that already several times with no success

Please describe what you did and what you saw.

You may need to erase the drive and reinstall OS X assuming the drive is OK.

Install or Reinstall Mavericks or Mountain Lion from Scratch

Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.

OS X Mavericks- Erase and reinstall OS X

OS X Mountain Lion- Erase and reinstall OS X

OS X Lion- Erase and reinstall Mac OS X

Note: You will need an active Internet connection. I suggest using Ethernet if possible

            because it is three times faster than wireless.

Did you start up in safe mode?