One day my refrigerator was doing well, and then all of a sudden I see a huge puddle leaking out of it. When I opened the freezer, almost everything inside was melted. Also, the refrigerator side was warmer than usual too.

I did the basic check of unplugging the refrigerator and replug it after 2-3 hours. Sadly that didn't work.

However, when I replug the refrigerator, I noticed that the motorish sound from behind it was making a softer sound than it originally was. Currently, my hypothesis is that the compressor must be broken or the fan is probably broken.

I would appreciate some help.

If its stuck in defrost mode it wont freeze so check that defrost timer and that will also kill your fans and compressor.

sounds about right, find that defrost timer and stick a screw driver in between its tabs and turn it until you here a click and see if those fans and the compressor start up before you start replacing anything.