Males cats are more at risk for crystals and stones, you should check him for these first because he could associate the litter box with pain. Maybe different litters might help, look at the link sugarcatmom posted you may find some answers to behavioural reasons for inappropriate elimination.
Do everything you can for your cat, I wouldn't advise giving him up because first it is difficult to give away a cat that is not using the box, and if someone does take him and he goes outside the box his new owners might not be as patient as you which is opening up possibilities for all sorts of bad things happening.
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