Clarify your topic, and address this: wouldn't all amino acids have a pKa associated with the amino and carboxyl group?
I'm trying to figure out which of the amino acids have no pka
OK.
and what it means if a certain amino acid has no pka?
What do you expect? What you expect, explains why you're asking, and helps us get to the bottom of what you might be missing.
Since some amino acids have more nonpolar side chains (example alanine or phenylalanine or glycine) than others, then shouldn't these side chains not have a pka?
You said you want to figure out which amino acids don't have a pKa, now you say you know the nonpolar side chain doesn't have a pKa. So what? Rocks, cars and people don't have listed pKa's, but compounds often do. You seem to be picking things apart at random, but why?