How do I remove stuck-on stains from laminate flooring?
Very few things can "stain" a laminate floor, the top coat is non porous and made with a silicon dioxide material that is very hard.  You can scratch or gouge them, or get water between the joints that can bubble, but staining is very uncommon.

You don't say what you think the material is so it is difficult to recommend a solution.  "Melted ice cream" sounds like possible paint drips.  Try carefully scraping with a plastic putty knife or finger nail, and work up to a razor blade being extremely careful not to gouge the floor.  Once you have the majority of the material cleaned off try household cleaners, or a paint and grease remover like "Goof Off" (available in the paint section of most home stores)