Most computers allow you back up or download data from hard drives. This can be very useful if you want to transfer large amounts of data easily, or if you want to make sure you have all the data saved that you need in case your computer crashes. There are several different ways to transfer data, but not all can be done when your computer screen fails or when you can no longer read the display for some reason.

Scheduled Back-Ups

The easiest way to ensure that data is backed up when your computer display screen is dead is to already have a back-up system in place. There are several different kinds of software that allow you to schedule back-ups from your hard drive. Some are included in operating systems, while you can download others free online that will allow you to make more detailed instructions. Usually, this requires an external hard drive, unless you have a back up hard drive already installed on your computer. Once you have a hard drive set aside for backing up files and the proper software, you can schedule back-ups based on intervals of time. You can schedule back-ups to be initiated every day, or week, or month or all three with a different priority of files set on each. The hard drive will then already be updated with recent information even when the display is absent. If the display is the only part of the computer system affected, then the automatic schedule will probably back-up files at the appropriate time anyway.

Sudden Display Failure

If your laptop screen has broken and you are wondering how to back-up files, most laptops include display ports that allow you to hook up an outside monitor or television screen so that you can still back-up files by using the operating system capabilities. You can also swap out monitors for desktop models, but if this doesn't work, then you may have a more serious problem which renders backing up files impossible. You can also do the reverse and remove the hard drive from your computer and put it into an empty slot in another computer--most computers have removable hard drives that allow you to swap them out. If you have a Mac, then you can use the Firewire port with another Mac computer and, as the computer begins, hold down the "T" key, which should initiate a target mode. This will allow the functioning Mac computer to view the screen-dead version as simply an external hard drive, allowing you to safely copy transferred files.

Source:

LifeHacker: Geek to Live: Automatically Back Up Your Hard Drive

Tom's Hardware: How Should I Backup Data From My Broken Laptop?

MacRumors Forums: Broken Screen and I Need to Back Up Data