Yikes, that's a long time for this to be going on. How many litter boxes (covered or not?) do you have and where in the house are they? What kind of litter do you use? There are a number of reasons cats stop using the litter box and it always means that something isn't right in their world, whether that be medical or psychological. You've ruled out the medical possibilities, so now it's time to look at what else there is. If there is only one litter box, you need to add at least one more, if not 2. Put them in different parts of the house. Try different litters. If the box is covered, try one that isn't.
How do the 2 cats get along? Any tension that you've noticed?
You should also try to find a product called Feliway. It's a synthetic pheromone that mimics the "happy" scent that cats rub on things with their cheeks. Makes them feel at ease and can help if there are stress or territorial reasons for the peeing. Comes in a spray and a room diffuser. I suggest getting both.
Here are some links for you to read regarding inappropriate elimination:
Please don't take him to the pound. It would be a death sentence for him and it would be kinder of you to just euthanize him yourself and be there for him while he dies, instead of alone and under traumatic circumstances. But there are still options, so lets see if we can figure something out.
Oh ya, just want to make sure - he is neutered, right?