"Mis padres todavía no son viejos."
Translation:My parents are still not old.
That's a good one, and your brash question is noble, or ignoble! It's poetic and dramatic, getting the best of both expressions. Use it in the real world! In grammar cocktail parties with linguistics professors, however, they find it terribly redundant, and frankly, a little droll, since it violates the preferred usage of "yet" with the negative. Did you get my drift and my meaning all rolled up in one?! ; ) Who's still not rock and rolling yet? Let's go, Rock and roll!
Still means a state that has existed for some time. I was working 5 years ago, and I am still working now. If you say My parents are still old, means they were old for some time, and they are still old now. Just sounds weird, and if you mean they are actually quite young, you should say: My parents are not yet old. My parents are not still old, could mean they are now dead, because of the negative, not... Just my opinion.