My intent isn't to have sex with her actually. I just want to be in a relationship with her. That's really all I want. And are you saying that if she is showing interest, I can go from there simply by talking to her and showing interest myself? Or is there something more to it?

You are mixing up Likability, Trustworthiness with Sexual escalation and Intent.
Now by definition being likeble and trustworthy you are already falling into the friend zone.

What you need is not she like you. Its to show her that you actually have a "dick"
Showing intent doesnt mean you have to be loud, doesnt mean you have to be a dickhead or a dushbag, its just mean that you let her know that you are interested and you are being a man about it.
You are probably just engaging her in a very logical way and not getting enough into the kino.
Again im assuming a lot.

The following videos might be harsh but that the dark reality of the game:

http://www.youtube.com/watch?v=mo0d10Tl ... RaneAlfSGg

There really is no concept of a girl "liking you for you". She either likes you for your looks, or your money, or your ability to entertain her. Some girls might like hanging around you because you make them laugh, or maybe they like riding in your car, hanging out with your group of friends, or it could be that they think you'll be able to provide for them financially and they'll get nice things from you and they won't have to work as much.

What I recommend is using your words, instead of your actions, to flush out their true intentions. Don't just stop paying for shit all of a sudden, because that could fuck up your frame/reputation. Instead, drop little hints that the things she is accustomed to will be coming to an end soon. Then judge how she reacts. Tell her a check you were expecting didn't come thru, or a real estate deal didn't close, or you lost a lot of money on a stock trade. Act stressed out about it. This is the time when she should console you. If instead of consoling you she starts asking questions about when you are going to be getting more money again, and doesn't seem the least bit concerned about your emotional well being, then you'll know this girl is just looking for a free ride on your tab. And to be honest, most girls turn into gold diggers once they get with a guy who has money. But test her just to be sure.