Re: Why will plants grow in Diet Coke and water and not other sodas?

I think you are correct that it is the sugar. I looked at a bottle of 
generic soda pop and the label said it had 30 grams of carbohydrate 
(sugar) per serving and 8 servings per 2-liter bottle. That would be about 
120 grams of sugar per liter. That's a lot of sugar.
The dissolved sugar makes the water in the soda pop less available to the 
seed, and seeds need water to sprout. 

The Diet Coke contains no sugar. Instead, it has an artificial sweetener 
that is much stronger than sugar so only a small amount of the artifical 
sweetener is added to the Diet Coke.

If you did a followup experiment to test your hypothesis about the sugar, 
you could add different amounts of sugar to water and treat the seeds with 
those sugar solutions.  You could try 25, 50, 100, and 200 grams of sugar 
per liter. Seeds might sprout at the lower sugar concentrations but not at 
the higher ones.