Just what is the purpose of the styrofoam? Is it for sound conditioning in the basement or what? If it serves no purpose, I would remove it and do your finished wall right over the existing cement walls using masonry screws.
Believe me, the strofoam is not a soundproofer and definitely not a good weather insulator, so if you are not recording Garth Brooks or Shania Twain in your basement, I would axe the styrofoam all together.
That's my story, and I'm stickin to it.