It might possibly be a jade plant having a near-death experience.
It took 14 years to get there, so this is one tough little plant. Sad to behold now, but it's still showing some signs of life. Here's what I'd do:
Do NOT repot now, and don't pull any parts out to look at the roots.
The cutting will show new top growth when it roots, I wouldn't move it now.
Do not fertilize now.
If the soil is now repelling water, it has become way too dry. The best way to overcome this is to give the whole pot a long soak in a bowl of water. At least an hour, until the soil is re-hydrated. Then drain the pot well, tilt to get as much water out as possible. Don't water again until the soil is almost dry, maybe several weeks. This is assuming the pot has drainage holes.
I don't see any parts I would trim off now. The little stub that is dark on the tip should just naturally dry up, no need to create a wound.
Yes, by all means use the grow light, and your best windowsill. I don't know what kind of grow light you have, but this plant needs a lot more light. Start slowly, a couple of hours a day, and gradually increase. In our Arizona winter, my succulents get all day in a bright south facing window, AND 16 hours of daily grow light. (Sorry, Canada!)
See how it looks in Spring, decide then whether to repot. If you do, I'd use a much smaller pot, with lots and lots of drainage holes. The grower's plastic pots work really well for me. The ugly pot can be placed inside a prettier cache pot, just never leave it sitting in water.
I'd try a different brand of cactus/succulent mix, without peat moss if possible. Add some additional grit, chipped granite poultry grit is my current favorite, but you can also use small gravel, pumice, or large, screened & washed perlite. I make it about 30% extra grit for succulents, more for cactus.
Remember that repotting will stress the plant and set it back a bit, don't be in a hurry, and disturb the roots as little as possible. For right now, I'd leave it alone except for more light and getting the soil hydrated, see how it does.
Also, how are your temperatures? These plants like it bright and warm. I've been having some success with a heat mat and thermostat set at 80F. (26C.)
Improve its conditions, give it time, and see how it does. Please let us know!