Does she like me or is she playing games?

i don't think she's playing games. but I don't think she's very intersted as anything more than friends. the carnival thing didn't count as a date; from a girls point of view. she probably said the buy her ice cream thing to make you feel better about not paying for her entrance fee or whatever. but she paid for herself because it was casual hanging out, not a date. she may not be ready for anthing more than a friendship right now, which is probably why she;s been "really busy" the past month. when you asked her to the movies, well it just sounds more like a date right off the bat. than just hanging out. which probably made her nervous cause she doesn't want more than a friendship, so she's been "busy" and hasn't had time to go to the movies. she probably does have the time, but she's thinking you'll take it as a date even if she doesn't and doesn't want to lead you on. maybe start hanging out in groups together. like you her, and a few other mutual friends. that way you guys can get to know each other and she won't feel any pressure from you to go out on a date or anything. and who knows, maybe later it will turn into something. but for now I'd say just let anything more than friends go. cause I don't think it will happen at least not soon. but maybe later?
i hope I helped, or at least gave you a girls perspective on it.

Your gut feelings would tell something. If she seems like she isn't interested, then forget about it. If she responds or calls back, or anything, then don't act as if you won something here.

I'd suggest you move on and find other girls.

Let her go. If she's interested at all, she'll call you. If she does, don't act too excited that she called. Be a little weary, she sounds flakey and is quite possibly playing games with you and maybe another guy. And if she likes you, you won't find out until you ask her if she does. Women, they come and they go. Go out and meet someone else. Play the field.