Cat who refuses to litter box train?

[wife of marine]

I have a kitten/cat, old enough to be litter box trained but still young. Keep in mind that this is not my first cat and we have litter box trained several cats in the last 15 years. This is the first case where the cat will not use the litter box. He goes all around it, but never in it, and wherever in the house he feels like going. We have tried switching litter and since he was originally an outdoor stray we have even tried putting a little dirt and grass in the litter box. He just doesn't seem to care. For 2 weeks now we have placed him in the litter box several times and not let him out until he goes. We praise him and a few hours later we do it again. It's in the middle of the night when we have problems and it is affecting our other cat who can't stand the mess in the litter room and goes in there and meows his disapproval. This morning I found 3 piles under my daughter's bed (2 old and 1 new) and another one 6 inches from the litter box. My daughters are having a slumber party this weekend and their bedroom smells terrible.

Has anyone ever had a cat that just wouldn't litter box train, no matter how patient you tried to be and reassuring when they do good?

Cleanliness of the litter box is not an issue. Even with 2 cats we keep that litter box very tidy.
I have already tried most of the ideas already mentioned. I have had up to 3 cats at one time before and the one litter box was never an issue because it was cleaned out at least twice a day. I will try a small litter box just for him and see if that works. Some cats hate having their food by the litter box so maybe if I move the food to the litter room he will be more likely to use the box to keep it away from his food and water.