Initial post was not very clear in the intent to not fix this computer and only concern for the data on it. If your going to connect this to another computer solely for the data on it vs using it as a bootable drive then the video card has nothing to do with your problem. Its either a healthy drive or not a healthy drive. Connecting it to another computer using an external drive case or caddy will prove if the drive is good or not, and I would suggest running crystaldiskinfo against the drive to check its health. Standard edition portable ( 4.6mb ) is the one I use. You download this on a healthy computer once you get one to replace this one, and then connect the drive from the old computer to new computer, then run this and it will check the SMART info on all hard drives and SSD drives and report back the health. If all is green all is good and you might just have some data corruption, if you see a warning then the drive that is yellow with a warning is either running with damage or is failing due to sluggish behavior that was detected by its self check on boot that all modern hard drives and SSD's have.
Be sure to scan this drive for virus's and malware before using any data on it just in case its infected, you can avoid infecting the other computer.
https://crystalmark.info/download/index-e.html*** Its sad that that computer might go over a cliff and other than a corrupt install of the OS in which the video cuts out, it may be an otherwise healthy 8 year old computer.
To me its like sending a car to a junk yard when the timing is just off, set the timing and back up and running... analogy to timing being a healthy OS environment will probably cause this system to run healthy. A bootable Linux Disc if available would have been a dirt simple way of testing the video card and rest of the computer hardware as healthy as for modern Linux Distros support about 99% of the video cards out there or have a generic driver that works.
