How can you tell the script doesn't run? After double clicking on it, does it enable Adobe World-Ready Paragraph Composer? If not you can do it manually in the Paragraph panel flyout menu. Here's some more information about it: indic « Caveat Lector. By the way what font are you using?
Which hyphenation dictionary are you using? I have found that in many languages, there is enough divergence in spelling that some words simply cannot be hyphenated, because the hyphenation dictionary expects one spelling and Every Single Speaker of X Language On The Planet expects another.
Also, sometimes InDesign has a hard time recognizing a term typed with combining marks as the same word with precomposed characters.
Lastly: Have you used the settings in the Hyphenation pane to try to force different breaks? I think that the default settings are not appropriate for Malayalam, and I would myself only hyphenate long words. So the default settings are, I think, to hyphenate no fewer than two letters away from a word boundary, in any word with more than five letters. I'd bump that up to words of no fewer than, perhaps, seven to nine letters? And increase the letters-from-word-boundary to 3 or 4. That way only long words get hyphenated.
I am using Malayalam hyphenation