[pushkins]

As long as the paint is firm to the wall and not flaking off you could just re paint with a good quality latex paint. Preparation will be the key to a good job, clean the surface down well before applying a new coat.
You could also paint with drylock a water barrier paint if you want to try to stop the moisture entering the basement.
WARNING: drylock will give a very textured finish to the walls that is not easily removable, so think carefully before taking this option.