I doubt distilled water will do anything; it's value is limited to eliminating mineral contact so AFAIK it is prophylactic at best. If it is a hardened soap film or similar, I would try a solvent. Xylene is used to remove industrial coatings and IIRC is safe on glass. If it is mineral deposits, that can be extra tough. Deposits can react with other chemicals and create a film or scale that must be removed first before you can get to the mineral. I'd try (real) TSP, or maybe Calgon. Or Lime-Away. Pls do keep us posted.