Getting in here late, but the easiest (?!) way to find the odds in such complex situations, which would defy easy expression in enumerative combinatorics, would be to run a Monte Carlo simulation. I have done this a lot of times for various games and if you run maybe ten million hands you'll get something pretty close to the correct odds. "All" it requires is some computer programming knowledge and experience. (No, I'm not volunteering to run this one.)

That would apply to the odds of getting a hand with no intial meld. Getting a totally unwinnable hand requires playing out entire games, and depends on the opponent's play too, so the problem is too broad to solve except with sophisticated machine learning techniques.