Yes, this is a big ask, especially for anyone who hasn't ripped apart a computer before. If you can see that drive's files on the working computer, pull out anything essential and make copies. Once you've removed the drive, plug it into a working computer. Lots of PCs make this easy, but for any device, the process will be easier with a tool kit and universal drive adapter. To make sure it's the hard drive and not one of the many other things that can go wrong when starting up a computer, if possible, remove the hard drive and plug it into another computer.
This works differently depending on whether you have a magnetic spinning disk drive or a solid-state drive (SSD), which you'll find on most modern computers. Your computer mostly erases the information that points your computer to that chunk of data, which will remain until it gets written over. The good news? When you delete a file on a drive, all that data doesn't immediately go away. Any actions, even installing a recovery app, risks overwriting the files you need. The first step: Remove the hard drive from the device if possible, or otherwise stop using it.