Well I've dated this girl the last week or so, she started being quite forward texting me everyday asking how's my day going an stuff, this was before we actually dated, which I found a bit forward but thought nothing of it. This girl also suffers from depression which she told me on the first date which wa a bit of a shock but its not a big deal to me. The date itself was great she admitted feeling very comfy with me an asked me at the end of the night if I wanted to see her again.
She kept up the texting the next day and wanted to see me the day after this which I went along with. Also she told me she had told her friends and family about how great I was. Now this is where it gets strange whist out with a friend she seen her ex who she split with 9 months ago with the girl he cheated on her with and she wents nuts, she told me this. Now the next date she is texting me all day saying that she's really looking forward to it but she didn't get much sleep so she's going to catch up on some.
She later turns up at my house and proclaims that's she's in a bad mood and told her dad to kiss her lol. Well we went out anyway and she was clearly in some sort of a mood, at the end of the movie she apologised for not being her usual bubbly self and would I mind if she went home, so I just said no problem see you soon. We had a brief chat and kiss in her car, then she went. She texted apologising again which I replied saying don't worry about it. But we arranged to meet up later in the week which she said would be good. So I left it a few days then text her asking how she's doing an such and got a reply of I'm great just really tired, and that's all I've had since, she's great but really tired.
No mention of going out from her at all, now on my birthday which was a few days later she sends me a message on a social networking site saying sorry its late, happy birthday, I've broken my phone. Now from this I thought oh well a polite she's no longer interested. Then a week later on the same social networking site her friend asks how she's doing and anything? You know, to which she replied nah, I give up! Mustn't be interested. So I've sent her a couple of texts an emails in case she thinks I'm not interested and she is totally ignoring me now. What is this girl playing at?

Who knows, but it doesn't sound like much fun to me. If you have had enough of her confusing drama, have a talk and get answers, or stop dating.

Sorry, I'm not sold on these social network connections, but seeking answers, and not assuming, would be my thing to do.

Sounds to me like she could be looking to you for her emotion strength and she sounds like she could end up being the clingy type.
I wouldn't get too involved with showing too much feelings toward her until I felt more comfortable with her cause it sounds like she could read too much into it.

Thanks for the answers, they have given me much to think about. Still confused though why all of a sudden she is totally ignoring my calls, emails and texts.

If she's ignoring you, she's just not that into you. Move on. Plenty of fish in the sea