Verified answer

this is not a medical problem at all, its down to the training and behavior of the animal. obviously the cat has not formed a strong enough mental link in its mind to use the litter-box, and it has not learned proper grooming skills from other animals since it seems to be on its own. it also sounds like the correct diet for the animal has not been found, or there are stressful factors that inhibiting natural digestion and defecation.

as for the caked on feces, thats down to poor grooming on both your, and the cats side. if you aren't prepared to clear these problems, then don't own the animal. this is such a simple problem, yet the first answers states you should take the animal to the vet, for what is purely a cosmetic and a behavioral problem.

please for the love of god do not take up any animal that you are not 100% capable of caring for!

please do me a favor and take your cat to the vet