What happened to Elsa and Anna's parents .

Yes... if only they had Elsa along with them, then this all could have been prevented (had she been taught to control her powers properly before this all happened).

She would've been able to freeze the water or something similar and save them from their death.

Elsa needs a time machine now! Quick! Go to the past with your knowledge and fix everything!

This would be more of a quiz question,but...
they died on Ariel's ship, just sayin'.

Did you not pay attention in the movie when they got on the ship and got caught in a storm and their ship sunk? Well,anyways that the answer to your question.

There ship sunk In a storm. btw I thought it was weird elsa wound'nt even get out to go to her parents funeral.

The ship was engulfed in waves.