I came into the college library & sat down at a cubical that had a jacket on the chair next to it, on the off chance that the jacket belonged to a HB, in which case I wouldn't look like a creepy guy who came and sat next to her when there were lots of empty cubicals.

What now? I asked her about whether she could get a wireless signal, but that's all my little brain has come up with so far. She is paying me no attention.

I tried first leaving a message for someone using my cell phone, so the sound of me talking wouldn't be so abrupt, and then hanging up and saying to her, "My final exam is in half an hour. Think I should start studying now?"

That went very poorly. I couldn't get any eye contact first, because of the way the study carrolls are set up, and she didn't even realize I was speaking to her until I was almost done with the sentence. My intonation was crappy, totally lacking energy, and she just looked irritated and/or scared.

Definitely shouldn't have opened asking her if you should start studying for an exam. Been in cubicle situations before and I have always found that getting eye contact is key before progressing into conversation.

If she's sitting next to you, turn slightly and look past her. She'll likely turn and look at you. Catch her gaze, hold it for an extra split second and turn back to your desk. After a few seconds, turn again and look past her. If she doesn't turn and look at you again, turn back to your desk. Again, after a few seconds, repeat the same process ... She will turn, catch her gaze as you start moving your head back to its original position, but instead of turning back to your desk, start talking. Ask about her coat, top, bag, something ... Anything to get her interested. You can start to exchange notes after a while since it is a library after all ... Touch her shoulder when you have a note for her ... It's kino, it's playful, it works.