I had an interesting situation -- first turn of the game, I didn't have any cards in my hand matching my goal color. So I played "Trade Hands" with the next player instead.
He was stuck with my cards, and a Silver Dragon that was already no longer wild, and he didn't draw anything suitable either.
He had no legal play. It's not addressed anywhere in the rules. He ended up just skipping his turn.
I'm not sure I understand your situation. You are not ever required to play a card that matches your goal color.
My earlier post was wrong. Here is a quote from the Aquarius & Seven Dragons FAQ
* Q: Can you pass?
* A: Yes. (In Aquarius, you might have no other choice during the earliest stages of the game.)