It does sound as if your cat is responding to the dirty litterboxes, however cat needs to go to the vet for a check up just in case there is a medical problem. Very often this is what causes cats to urinate and poop in inappropirate places.
At any rate, you will need to take steps to retrain the cat to the box. Basically you need to confine the cat to a room like a bathroom, or a large cage with only food, water, bedding and the litterbox. As he begins to use the litterbox consistantly you can expand his space. There is more information at this link:
Litterbox Problems
Another thing you might try is putting a clean litterbox over the spot where he has been pooping and gradually moving it to the area where you prefer the boxes to be located. Be sure to clean the soiled spot with the suggested products listed below, however!
You need to thoroughly deodorize wherever the cat has been peeing or pooping. Petastic is highly recommended as is Heaven's Own. It is the smell of the "accidents" that causes a cat to reuse the place.
Check into using Feliway, a spray that mimics the happy scent cats leave when they rub their check against something. You can get it from your vet or from Cat Faeries at http://www.catfaeries.com
If you visit the website, you will see a phone number that you can call and for a fee discuss your cat's problems with someone. The person who does this is very knowlegeable and it may be worth the $$ for you. Feliway is also available in most large pet supply stores. There is also a plug-in with Feliway that can help.
Finally, if all else fails, ask you vet about using an antianxiety medication such as Buspar or Prozac. These very often work, however the decision to prescribe them will rest solely with your veterinarian who will be able to monitor the dosage and side effects.
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