Try a Mr. Clean magic eraser. That may cut the film, and then you can follow up using Windex or some other type of ammonia-based cleaner on the glass. I've had good results using this combination.

Try using soft scrub and the scrubby part of a sponge, get the sponge slightly damp so it will create a foam, scrub the entire surface in circular motion. May take a couple of times, but it will come clean. Once it is clean, use fabric softener sheets to keep the build up off.

Vinegar cuts through minerals in the water.

What finally worked for me (after going through vinegar, CLR, LimeAway, etc.): Barkeeper's Friend -- the powder version. Mix with water to form a thick paste, then apply to the glass, working small sections at a time. Wait a few minutes (but before it dries out), then take a utility razor and carefully scrape the gunk off. It took me a while, working at it on and off for a couple of days, but the glass was as good as new!

magic eraser, clorox bathroom cleaner (no bleach) fantastic and/or white vinegar.
i would spray with clorox or other soap scum remover or vinegar and then use magic eraser.....rinse, then use windex to shine....
you can also try bon ami mixed into a paste, scrub with magic eraser then rinse.....
i will say, if its really caked on, it will be almost impossible to remove completely.