My son didn't become potty trained until about his 4th birthday. I don't think it was his birthday, though, that did the trick. I think it was because I had answered all his mental reservations about it.
One day I asked him very specifically if there was any reason he couldn't put all his poop only in the potty all the time, and he came up with some reasons. I was able to answer them and take away his objections. I asked this same basic question several different ways, and each way he responded with some objections that I was able to address.
Lo and behold, he was 90% better by the next day and within a week he was reliably using the potty with few accidents, whereas before he'd had very little success. If you're having trouble, I think using a bit of psychology is worth trying.
One example was that he said he couldn't use the potty because it hurts, but I explained that actually it's holding the poop that makes it hurt: "You know how when you're hungry, eating makes you feel better, and not eating just makes the feeling of hunger worse? Well, when you have to go, it's getting the poop out of you that makes you feel better!" This made a lot of sense to him.
If this still doesn't work, take heart. Your child will use the potty when he or she is ready. But sometimes you can jump-start the process.
One more thing: the part about "when he is ready" is really the trick. You cannot force a child to use the potty. I think back when I was researching this due to my own concerns about his potty training, I read somewhere that the biggest impediment to children's potty is excessive parental coercion. Once it's a power struggle, the child is going to win it. Instead, make it his own choice so that he feels empowered by success in this area, instead of feeling like he lost a battle by using the potty.