I think this is a good illustration of "ignore her if she is being distant and decide 'if she's going to be distant, I will focus on me and what makes me happy" and, when you actively do that, she's going to understand that she needs to actively be someone you want to be with, pay attention to, etc.
This is an interesting situation tho. It reminds me how no one discusses their expectations prior to large life events. Why not have the conversation "what are your expectations for sex, attention, finances, etc, etc, etc" after we move in together?" It's akin to premarital counseling where the couple has the help f a therapist to determine if they are on the same page/compatible. Most couples dont do any of this, they just go in blind expecting that their needs are going to get met, and they end up unhappy and illl satisfied. Then you throw the inability to effectively communicate and compromise on top of that (b/c let's be honest, we all suck at that) and this is the prefect recipe for breaking up and/or divorcing.
You absolutely can try to strong arm your needs our of her. Do a 'soft next' or ignore her when you are feeling ignored and simply 'do you'. Thing is, she may not be able to synthesize your soft next/ignoring into the realization of a need you are having that is not being met, she may see you as being passive aggressive, and she may get resentful that you are ignoring her, and then start to act out based on that. then it's all a downhill spiral from there until chaos and destruction happens as you break up. Then you get to come back on these boards and have a lot of people say "see, I told you so, women are b1tches and are only good to pump and dump!"
The other route is to try to talk to her about your expectations and needs, allow her to do the same, and see if you two can be there for each other (you know, try to BUILD a strong relationship) You dont have o lose frame while asking for what you need. You state your need in the form of an expectation (do this gently but firmly) and see how she reacts. Someone who wants the relationship to succeed and wants you to be happy with the, is going to take you seriously and do their best to be the person you need them to be.
The determination of if this person is right for you starts with conversation. Communicating openly, expressing your needs and expectations in an effort to determine if the other person is all in or not, isnt popular on these boards. Take that into deep consideration.