Why is Randomness so Hard to Prove?

[Lestat]

Really bad at math here, but the discussion on determinism seemed to indicate we need quantum mechanics to prove randomness exists. I don't understand...

Why can't we just use the throwing of dice? Or any other method where results are unpredictable, uncalculatable, and seeingly perfectly random? What about random number generators in computers, etc. ?

I'm sure this is a dumb question, so try to go easy on me. It just seems to me there are plenty of things without determined outcomes. Why do we need QM to disprove determinism? One other thing that bothers me...

If everything were in perpetual motion, determinism would make more sense to me. But there are clearly things in this universe that STOP. Unlike the billiard break example that someone gave, my car for instance, stops... And then goes again. This would seem to disrupt the notion that all is pre-determined by some antecedent event. At least to me.