<human>: Summarize the given text in a few sentences.

I should probably post this on a throwaway but I'm lazy. I'll give some details to my situation so that maybe you guys and gals can have a better understanding for my question.
Back when I was in 8th grade I knew this girl and we never really talked. Just the occasional hi and a shared class. She was a grade behind and I ended up leaving the school the year she moved up to high school so I never got the chance to hang out with her and really get to know her.
She's a senior now and I'm out (I'm an odd case school wise, I won't go into detail other than I'm in a master degree program). I wanted to try my luck, recently single again and figured it wouldn't hurt to try. But my only way to talk to her was through FaceBook so that's what I tried. Now we were hardly acquaintances back then so I asked if she remembered me and to my surprise she did (or was just being nice lol). So we sent a few messages back and forth and then I asked if she wanted to go see a movie. Not a date, just a "Hey I'm going, it's a cool movie I've heard and I think you'd like it" and then invited her to a BBQ party I had about two weeks ago. To both she said she'd love to go but for the movies she was busy that night and she never replied to the bbq invite past saying that if she can she'd love to go.
So now we're at today and at my question. I haven't sent a message to her since the bbq party but I still want to try. Is what I'm trying at all possible? Should I message her again or just give up? If I do, what could I say?

Note for the curious: I'm a kind of shy type guy (duh) and she's the ol' cheerleader everyone loves and wants so in terms of popularity and attractiveness, she's waaaaay out of my league but I don't believe in leagues so yeah.
<bot>: Girl I hardly know, way out of league, get to know her and ask her out on a date through FaceBook. Possible?