But, that's the whole point! Why are you going for last resorts when you haven't even tried the first and most obvious steps? Why can't you just start up a nice, normal conversation? How on EARTH could she answer if she likes you? She doesn't even KNOW you. A few waves and hellos exchanged does not make for a conversation, it makes for politeness between two strangers.
You have two choices and only two choices here. You can either walk up, introduce yourself and start up a conversation to see where it leads, or you can walk away and just forget about it.
She doesn't know who you are other than some guy who sometimes says hi in class. If you don't start a conversation at some point, she STILL won't know who you are. That is all there is to it. If after all this time you still haven't worked up enough courage to just walk up to her and strike up a conversation, you never will. You're still making a thousand and one excuses why you shouldn't talk to her. If you need to make so many excuses, then just don't talk to her, forget about her, and move on with life. It's getting beyond pointless to keep repeating our suggestions to you of ways to start up a conversation.
There was a good point/question a few pages back. How well do you do starting up a conversation with ANYONE? Not just a girl/woman you find somewhat attractive, but someone sitting next to you in class, roommates, people waiting in line with you at the store, etc.? We know you are able to walk up to a professor and ask questions pertinent to the class, because that was the circumstances of you noticing this young lady. But, how good are you at small talk/chit chat with people you don't know and when it's not related to asking questions in class? If you aren't any good at it, and from your lack of ideas on conversation openers with this young lady, I suspect that's the case, then give up on her and work on these social skills you're going to need all throughout life. As people have already suggested, start talking to everyone and anyone you meet. Talk to people in line with you about the weather, talk to your roommates/housemates about some current events topics, talk to the person next to you in class (before class starts) about the upcoming exams or the amount of homework you're all assigned. It doesn't matter what you talk about, just learn to start conversations with random people. Walking up to someone who doesn't know you and asking if they like you is not a good way to get a positive response.