There are a coupole methods to make use of.
The first is connect the computer to another monitor type,
such as a television or a desktop monitor.
you can access your data.
keep in mind that if the problem is just that the screen is damaged,
you can actually get it replaced for rather cheap.
My laptop was 1200 dollars.
It would have cost that much to get a new one,
and 400 to get a new monitor from the company.
by looking online,
I found the screen for 120,
and had it installed in an hour for 40.
before getting a new computer,
if the only issue is the screen,
look into screen replacement and local replacement.
if you must remove the hard drive itself,
then you will need to open the computer.
Locate the hard drive,
and remove it.
It is that simple.
You will not need to have the monitor working to do this.
I`d suggest looking up the model,
and you can find an interor map showing exactly where your hard drive is,
and how to remove it.