The cable depends on the monitor & the computer.
Since the laptop appears to be toast, I'd remove the hard drive, put it into an external case, & plug it into the computer that you want to transfer the files to. I actually did this when my previous laptop's screen went dead (the laptop was almost 8 years old & not worth replacing the screen). The case needs to have the same interface as the hard drive & what the target computer has; USB is the most common. When you have finished & verified the transfer, you can use the now external HD as a backup drive.