If 80-ish is your hot spot, then it's not hot enough. 90-95 at a basking spot, with an 85F or so warm end, 75-78F cool side and night time drop.
This may be the root of the problem, but now, I don't think it's as simple as turning up the heat. The gecko is thin, likely dehydrated, and anorexic.
Revert the enclosure to a quarantine/hospital style. Paper towel substrate, with moist paper towel or cloth in the humid hide. Keep everything clean.
A vet is never a bad idea; upon physical examination they may find that parental fluid therapy is indicated.
To rehydrate, offer pedialyte, or other electrolyte solution in the water bowl, and also try to convince them to lick it off a syringe. Sometimes touching a drop to their lips will instigate this.
Hill's a/d, or ground up bugs/pinkies can be syringe fed in this manner as well to offer nutritional support until it eats on it's own.
Undertank heat is ideal in this situation as overhead heating is more likely to dry out the lizard. These are desert animals, but hide during the day to retreat to humid, subterranian microhabitats. Once healthy, overhead heating can be resumed if a natural environment is the goal; but such humid retreats will be a must.

The shed skin, is not an immediate concern at the moment unless you see some constricting around toes, tail, or irritating the eye(lids). Moistening the skin and gently rubbing it off will work if necessary.

Good luck!

Ian

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