Backup MacBook pro late 2011
I see 2 alternatives, if it won't boot…


Take the drive out, mount it in an external USB case, then you can back it up from any other machine that can read the drive.
If you have another Mac, mount it in Target Disk Mode



  If you have two Mac computers with FireWire or Thunderbolt ports, you can connect them so that one of them appears as an external hard disk on the other. This is called “target disk mode.”
  
  
  Connect the two computers with a FireWire or Thunderbolt cable.
  Start up the computer to be used as a disk in target disk mode:
  
  
  If the computer is off, start it up while holding down the T key.
  If the computer is on, choose Apple menu > System Preferences, click Startup Disk, and then click Target Disk Mode.
  
  
  When the computer has started up, a disk icon appears on the desktop of the other computer.
  Transfer files by dragging them to and from the disk.
  Eject the disk by dragging its icon to the Trash.
  While you drag, the Trash icon changes to an Eject icon.
  On the computer you used as a disk, push the power button to shut it down, and then disconnect the cable.