Laminate is usually made with wood fillers. They tend to swell if they get wet. And if they get really wet, they start to de-laminate. If that's what is happening to your floor, you might as well do it all over. You should try to determine whether the moisture (if any) in your basement is a problem or not. That will affect any flooring you choose. Vinyl handles moisture well, but tiles may not stick, and if there is moisture collecting under a sheet floor, you will eventually have to replace it also.
Vinyl sheeting can't be installed over the foam underlay. It will feel nice & fluffy, but the first pair of high heels will just poke holes thru it (same with furniture legs).
Well the current laminate is a little rough in some spots.
Since we do this all with words, a little more detail in things like this would be helpful. Pictures are also helpful.