Hello high\hgih, I am sorry to tell you that you've gotten a lot of poor advice in this thread. But I really feel for you, and that's why I am going to write this brief novel for you. I really hope you read it, because it will really help you and it's my community service for the week.

Also as you read this, remember to always be you. Don't try and act like a different person all together, try to improve your actual self so there is no acting. You don't want to be in a long term relationship where you have to put on a facade all day. But it is possibly to incorporate what I am telling you and still be you, so do that.
We'll start with the hard part first, the mental hurdles. Have you ever heard of the Law of Reversed Effects? It states the harder you try to do something the more likely it is you will fail. You have it in your mind this woman is 'the one'. You don't even hardly know her and are ready to pledge your life to her. You got to get that out of your head if you want any chance of being with her. If you don't believe me you could go ahead and tell her you think shes the one and see how quick she runs for the hills (please don't do this she will run, remember I am here to help

). This will cause you to fail for two big reasons. First, because you want it so bad you are going to mess your self up. You're going to be nervous and stumble on words and all sorts of things that isn't going to get you the woman of your dreams. Second and most important, if you are desperate she will be able to 'smell' that desperation. Desperation is extremely unattractive to both sexes (Am I right ladies of RIU?). Any good salesman/saleswoman will tell you communication is 90% non-verbal and only 10% verbal. Most of that 90% non-verbal is body language. If you're desperate it will show in your body language.
So if you want to get the girl you care about you have to not care. Sounds counter-productive I know and hard to do, but it's what you have to do. If you're not worried if she will go out with you, or go home with you (if already out), it will show in your body language.
Confidence is sexy, not caring of the outcome makes you excrete confidence. Remember, there are more women than men in the US. As cool, interesting, and funny this girl is there are 10 more cool, interesting, and funny girls just waiting in line to meet you. I'm sorry but I can tell you're not all that good with girls even before you said it. You have an attitude that any girl going out with you on a date is doing you a favor by hanging out with you. You need to get that out of your head immediaty. Actually stop reading, get that out of your head, finish reading. I'll wait. It gone? Good.
ALWAYS remember, you're doing her a favor by gracing her with your presence on a date! You're a totally awesome, funny, interesting guy with the best weed (Hopefully you're a member of RIU.), any girl would be lucky to be hanging out with you! So don't you forget that!
Now, for asking her out. It would be a lot more helpful to know how you are going to see her next, I read the entire thread but maybe I saw and forgot. Do you go to school together, are you neighbors, how are you going to next see her, because I am assuming from your posts you guys run into each other. The best way to ask a girl out is something unique and situational to the surroundings, gotta think on your feet and be cute, clever and funny. What I can tell you is do not just say "Would you like to get coffee with me?" She may say yes, she may say no. Don't give her that no option because you already know she wants to say yes. Here's something you could do, have a good and fun conversation with her, but brief only a few minutes. The conversation is going to go much smoother now because you're not so worried on the outcome, you're the cool confident dude who knows there's other fish in the sea (and it's going to show, and be super sexy). In the middle of the conversation say "Hey, I got to run. So, you and me, coffee at 7:00 at Coffee Place X. You know where Coffee Place X is at?" Hopefully you can see the giant differences between the two. In the second you are not asking as much as telling. Remember don't be a jerk, noone likes jerks, but being a bit assertive is attractive. It's extremely important that you don't demand she get coffee with you, that makes you a jerk. Just say it matter of factly like you know there's no other answer but yes. Then by following it up with "You know where it's at?" you make it much harder to say no. She has to either answer that question first, or ignore it which is unnatural and uncomfortable to do. She would have to really not like you to be like "Yeah I know where that's at, but I ain't going there with your ass", or "No I don't know where that's at, and if you're going to be there I don't want to know". Warning if she brings a friend with her you are deep deep in the friend zone.
Acceptable first date places are, coffee, drinks (I personally don't drink), joints and bongs, or something unique that allows talking preferable where you sit side by side or close not face to face. Unacceptable first dates include dinner, movies, unique things that don't allow interaction (sky diving, gun range, etc.). Dinner can be acceptable after early coffee or drinks if everything is going good, but I usually prefer to end the date early after a couple hours. Tomorrow is another day if the first date was really great. You want to sit close or side by side with your date, which is why dinner is bad. The table is a huge physical and mental divider. Non-sexual touching builds comfort and affection, you can't touch her with a table between you. I am not going to get into non-sexual touching here, but I will give you a video on the subject. Just a heads up Mystery is in the audience and briefly interrupts from time to time. But sit through his douche baggery and you will be rewarded with great information. I am not a fan of the pick-up-artist community as a whole, but that doesn't take away from the validity of this information. It's super important stuff. If you don't want her to turn her head away when you go in for the good night kiss, this is how you prevent that. Watch all the videos if you have the time, there's 6.
http://www.youtube.com/watch?v=2660xYRZlzI
Never over compliment. If she is cute, she's heard it before and you want to stand out. The occasional compliment is cool, but make it about something unique. You know how many guys told her she has the cutest eyes? A lot. Saying something like "You have an amazing sense of style, that dress is awesome." will get you a lot further than "You have such a cute smile."
The key to a successful date is be confident, be yourself, and most importantly be fun. If a girl had fun on a date you're going to go on a second date, if you want to. A great way to have fun is to playfully make fun of her, it even has fun in it. You don't want to be mean or be a jerk but playfully teasing her will be fun and make her attracted to you. For example I was on a date awhile back, and the girl I was with was wearing this crazy black and white plaid really retro-y dress. She looked really hot in it, I am sure she had a mirror so she knew she looked super hot in it, so I made fun of her and it was fun. "Hey 1950's called, they want their wardrobe back." She laughed, we went back and forth and she playfully hit me on the shoulder. If your date hits you she's basically hitting on you, unless she's like really beating your ass in which case you really took a wrong turn somewhere. In the middle of the date I did end up complimenting her dress cause it was really cool. On the way back to the car I grabbed her by her hand and said "Come on we're going to get you a sweet 1950's beehive to go with that dress," and lightly pulled her toward a hair salon. It was light-hearted fun that she laughed at, and I got to hold her hand for a bit without being creepy. Win-win.
I was going to keep on typing, then I hit preview post and saw how long this was already. So I am going to wrap it up. Just ask her out on a date, go out with her for 2-3 hours, build some comfort with a bit of touching, kiss her near or at the end of the date or at the moment if you get one of those. I know you said there's no such thing as the friendzone, but let me tell you there is. Unfortunately I've seen this friend zone, and friend I tell you it is as real as you or I. Do something cause you are about to hop on a one way flight to the friendzone.
Edit: Oh I forgot to mention, I am sorry to tell you but you really shot yourself in the foot drinking too much and getting sick with her. That is like a huge dating no-no. Believe me, no healthy woman in the world wants to take care of some sick dude. If you drink alcohol you better hold your shit. But she's college age so it's not the end of the world, just do what I said and you should be gold. But it was still super unattractive. Learn from it.