I actually think she likes you.
But she may think you don't like her. She may think she's in YOUR friend zone.
From personal experience, just because I've told myself that a guy I like doesn't like me back and I go onto the next guy, it doesn't mean that I don't like my guy friend anymore. It just means that I'm trying to not like him anymore by getting a distraction (another guy). So, what I would say to you is to go on and ask her out without asking her out. Take her out somewhere like a movie or something and compliment her. Tell her she looks beautiful or something and be a completely gentleman. Try and brush against her and flirt. Let her see that she's not a friend to you.
At the end of the night, you can kiss her on the cheek goodbye and be a little close to her lips when you do. You can ask her to do other stuff too, but make sure it's just you and her so she doesn't get confused with group activities.
She's not in love or married to these other guys she likes. She probably likes them and likes you too. That's always a possibility. I think that everybody's kinda right on this one: she's moving on, but she's still trying to make you jealous too. Maybe this is her way of getting your attention by proving that she's datable to other men so she can look more appealing to you.
If that rambled mess didn't make any sense, I'll try and simplify it: she still likes you, ask her out to the movies or something, flirt, flirt, flirt, and see how it ends up.