Reading your post it appears the drive with the lost files is from a Laptop Quote "So I disconnected my hard drive and connected it to another laptop but the drive letters look empty or occupying just a few megabytes"
What was the model and make of the Laptop the drive wouldn't boot in?
What is the model of hard drive, like is it a SSD or some other hard drive?
If the drive is an SSD drive then stop immediately and wait further instructions.
Can you download HDsentinel from here
https://www.hdsentinel.com/ and check the drives health.
So long as you were not using security like finger print scan or boot lock password you may be able to recover the files using Reclaime from here
https://www.reclaime.com/If it is a SSD drive then stop immediately and wait further instructions