If the freezer is freezing, but building up frost inside, then it’s not the compressor. The unit is “working”, but it’s not staying frost free.
What has happened is the drain line from the freezer unit has become clogged, and the machine’s attempts to “self-defrost” are causing more and more ice buildup in the freezer. (Your coils may be dusty, too. The coils are on the back or bottom of the refrigerator. That’s where the unit gives up the heat that it extracts from the things you put inside. If the coils build up too much dust, then that insulates them and makes the whole machine have to work harder to extract “and give up” heat. In other words, some of the heat that it extracts goes back inside the box.)
Your refrigerator should have a tray at the bottom that (when things are working properly) may have a small puddle of water in it from time to time. This water evaporates into the room, and indicates that the fridge is working.
What happens on a self-defrosting refrigerator is that the freezer allows the frost buildup along the edges to melt a little bit every hour or so and drain down to that tray. That keeps the frost from building up. When the drain is plugged, the frost still melts, but now it can’t drain, so it re-freezes and continues to build up.
Find and clear that drain line, and the fridge will probably work fine.
But I’d also recommend that you consider a newer one. It will run more efficiently, probably have features that you’d like a lot (even without “in-door water and ice dispensing”) and be quieter to boot.