Just at least want to be friends with this girl (Sort of a long background to this)

Alright, so there is this girl, we've sort of known each other for about 2 or 3 years, but we don't really 'know' each other if you know what I mean. We've ever really met, we just know each other's names and faces, see each other around school (we're both 16), the only reason we know each other at all is just because I added her because we had a bunch of mutual friends a few years ago. So, we're not exactly friends, we just kind of know our names and faces.

Since I saw this girl, I just knew that I really liked her and wanted to be friends with her, maybe a little more than friends. She is very pretty, we have very similar interests, and everything (like hockey for example. We're both big fans of the local NHL team). It wasn't until (just looking back at my Facebook message inbox) March of this year we're I finally decided to start talking to her. I was just trying my best to make small talk. I said "Hey, you play lacrosse right, how's that going?" just things like that, and every time I just got really short, uninterested sounding replies from her, and even if I kept replying to hers, she would only reply once or twice and then stop.

Finally in May, I finally decided to ask for her number to try to talk to her more. I know that this was a mistake, just because we don't know each other well, and because she sounded so uninterested. But she replied saying something like "Sorry, I can't give my number out" which I know was most likely a lie, just her way of saying no. (To be honest, I would've preferred some honesty with just a simple "no", instead of lying, but whatever).

So, I know that I sort of messed up, or rushed it at times trying to talk to her. But honestly, all I want, more than anything is to at least just be friends with her. She is very quiet and shy, so she's not always very easy to talk to. I'm not really friends with her friends and vice-versa.

I just want some advice on how to at least get her to be friends with me. It's not going to be very easy based on the reasons I gave above, and I have a feeling she will just think I want to try to go out with her again or something.

How can I do this? Any tips, suggestions, advice or anything is much appreciated.

If you're still reading up to this point, Thank you, and if you're going to post tips or advice or anything in reply, then thank you in advance.

There's nothing wrong with asking a girl for her phone number. That wasn't a mistake.

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But honestly, all I want, more than anything is to at least just be friends with her.

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I don't think you're being truthful with yourself here. You only want to be friends so you might have some sort of chance with her. You have a crush on her, so any friendship is going to be kind of a farce. If you don't believe me, then ask yourself why you want to be friends with this girl. Because she seems interesting? Okay, lots of interesting people out there. Why this interesting person? Why is a friendship with this person so important to you that you'll ignore all the blatant signs that she's not interested in friendship and keep trying to force one?

You didn't do anything wrong with the way you pursued her. I can't really pinpoint anything giant errors that you made. You were interested, she accepted your friend request, you tried to chat her up, then you asked for her phone number. You made moves. That's what you should be doing. She's just not interested. On to the next.