Disclaimer: I'm tired but can't sleep, so everything I wrote below is part "essential concepts" mixed in with "examples of what I'm talking about, kind of rambling", so hope you can get something out of it

Editing it down to make more sense would require the kind of brain power I can't muster right now, heheh...
Qualifying is what you start doing to punish. Everything is a sliding scale. If they are only misbehaving a little bit, it can be a little joke at there expense, but still funny. If they are being very evasive or even a bit rude, then the qualifying could be as extreme as, in a light hearted way, putting some aspect of their personality into question.
Just recently - a girl approached me, we were having fun, but I played it too cool and went for a facebook instead of phone number and left quickly. I see this as a fail, I messed up the initial interaction, game over. She was cold on facebook. But, even though I fucked this up in the beginning, I still managed to get her talking on facebook, which she kept insisting is not her thing. Eventually I called off the conversation because it wasn't going anywhere but the way I actually got her talking even though she was trying tto avoid me was by putting her personality into question - in a light hearted way.
She never replied to my first two messages (and they were good ones) so I called her out on the behaviour, wondering if this was the same girl. She insisted facebook was not her thing, and she's just been lazy and doesn't get on facebook much at the moment. I told her she doesn't have to make stories to get me to stop emailing her like "those other guys", just tell me to stop and I'll stop. Then I asked her if the crazy girl i thought I met was all an act to collect facebook friends - if so, she doesn't get to keep me as one

I added "This is important." She sent 3 paragraphs explaining herself. I replied again, she sent back another 3 paragraphs explaining herself, this happened 3 or 4 times. Sure this didn't end up going anywhere but for someone who saw fit to flat out ignore 2 very positive and funny emails, I think this is pretty good results for such a weak connection (i.e. text, as opposed to voice or face to face) - no way would I have been able to make something happen at this point, before I knew how to qualify. Especially over text. Eventually I put a few funny things in for her to go off, to make the conversation interesting, but she wasn't taking the bait and she was making the conversation boring, the attraction wasn't there anymore of course - so I decided it was a dead end, and called it off - said I'm giving up trying to get to know her on Facebook, and told her about a dress up thing I was going to, and she can meet me there, threw in a little in-joke, and left it at that. I kinda might have been a bit too blunt at the end, although she seemed like she was trying to put in as little effort as possible towards the end - while at the same time I had an email convo going with another girl who was reciprocating very well to all the fun suggestions I put into my conversation, and we're actually meeting up on the weekend, so I couldn't have been bothered putting all the effort in when there's a girl willing to meet me who seems to know how to actually have fun. So - this wasn't the BEST example but it's the most recent one.
No one likes to think that their value is dropping in anyone's eyes, even your worst enemy you want them to think you're awesome and be jealous of you. So start to question something about a girl and she'll come to her own defence very quickly. Once you've got her talking, and you're challenging her, you can rescue a situation and make things interesting. If you can challenge a woman's mind, she feels like you're smart and can handle things and she feels safe.
It's all a sliding scale - right at the other end of this scale, she's calling you and asking to catch up cause she needs company, etc. and you should respond with generosity and fun. At the other end of the scale, she's getting pretty disrespectful, so you're qualifying her hard, for fun, and waiting for her response. And somewhere in between you have little jokes at her expense when she's getting a bit testy.
Basically it's all about feeling what she needs at the moment - reward or punishments, and what level. And that's the art - you can only just keep trying this and learning from experience, there are many variables such as your personality, her personality, the moment you're both in, things that have happened, things that may yet happen, etc. so like a lot of other things, it's not so much logical thought as it is experience and feeling your way through.
Never act out of anger. A neg done out of anger will really make the situation shit. Always be strong in your goals and comfortable with yourself no matter what the outcome is - that stability and lack of concern about the outcome, is one of your selling points. I know what I want, I'm going to shoot for it. When I was qualifying that girl in the email - I knew in my head that I'd won and lost heaps of girls, and none of them were won by fawning over someone who wasn't doing anything to deserve it, so get to the point as much as possible, have no fear in being direct about what I'm after, and be realistic about it - all the while I kept asking her things trying to find out if she really was this crazy girl i thought I met, or was it all an act - if the latter, I was going to lose interest very quickly.
Okay that was a huge ramble, I'm just going to post this and then start a new post to answer your initial situation more directly, because after reading it again I think I see it in a different way.