Nature's Miracle takes up to two weeks to work. Be careful, because if you use too much, it can leak into a room below or spread the problem. The cat may have urinated on the blankets - for some reason, one of ours does that sometimes or in baskets of laundry. The litter box needs to be really clean. We've had luck with the pine litter.
If you do pull up the carpet, you may need to replace the plywood underneath. For concrete and even new plywood, consider painting with Kilz to reduce odor if the problem is more widespread than you know. Otherwise, replacing the carpet won't make enough difference.
One of my cats won't use a litter box so I let him out every morning. If it is cold or wet, he comes back in quickly. We only have problems now if it is icy. Then he prefers the bathmat which is at least an easier cleaning issue. He does have a problem with a rug in the family room. I have solved this with feliway cat pheromones - a plug in item that looks like an air freshener but the odor is not noticeable. Somehow it calms the cat and prevents the problem. I know for sure that it works because the cat starts creeping around the rug when the liquid has run out and it is time to change it. But it is expensive.
Good luck.