What can it mean if a girl you met recently tells you that she's stressed and has problems, but when asked what they are, she doesn't respond or take the time to tell you what's going on?

She probably means that it's noneya.

It is one of two things. First would be she is worried about something and isn't ready to talk about it yet. The second would be she is on of those people who like to have people feel sorry for her and tells them this to do so. She then uses those people. Because they feel bad for her they are willing to do or get things for her.

You will have to decide which one she is. If you know someone who has known her for awhile, ask them.