You can't use your laptop display as a monitor for the desktop computer, if that's what you are trying to do. The cable you got is to connect an external monitor to the computer that the USB cable is plugged into.

What you need is a SATA to USB dock with external power, so there is enough power to run a 3/5" hard drive.

Here's an example, there are lots of different brands available from lots of different places online.
https://www.amazon.com/SSK-Aluminum-External-Duplicator-Function/dp/B07WS59SP4/ref=sr_1_13?dchild=1&keywords=sata+usb+dock&qid=1607561256&sr=8-13

This will allow you to take the hard drive from the desktop computer and connect it to your laptop. Then you can browse the drive and look for files that you want to recover. Windows will probably prompt you to take ownership of the files.