You've been dumped by your ex girlfriend and now she's giving you the cold shoulder like nothing you've ever seen. You've done nothing wrong, yet she's treating you like something stuck to the bottom of her shoe. Where's the logic? Where's the reconciliation?
What you must realize at this point is that her attitude towards you at the moment is more of a self protection mechanism than anything. In fact, you should not be taking this personally at all – there's a very good chance that you've done nothing to deserve this sort of treatment.
Still, it is what it is and it is something that you must deal with. While you may think that nothing is going to get through her tough exterior, if you step back for a minute, have a little patience, and really think about what's going on, you can take steps to remedy the situation.
This involves playing your long game. It is not for someone who has no patience, needs the relationship back yesterday, and can not function without their ex-girlfriend. No, it's going to take perseverance, patience, and the confidence that things will get better.
Give her some time to cool off. You'd be surprised what a difference a week can make. Treat her with respect (even if she is treating you with none), let her know that you will be there as a friend if needed, let her know that you're not trying to force her into making a decision, and make sure she Realizes that you have no ulterior motives (even if you do).
By completely taking the pressure off, she's going to be knocked for a loop. She is fully expecting you to be devastated and to start acting desperate and needy. She's expecting you to come to her begging for another chance. When that does not happen, it's going to throw a huge wrench in the works.
When you do establish contact after a week or two, do not bring up the old relationship, do not make a pass at her, and definitely do not tell her that you are still in love with her. It's tough love, but you have to take the wind out of her sails before she will listen to reason. There's no other way to do it.
Bide your time, have patience, and you are almost guaranteed to see tiny sparks of affection and desire again. The key is to not rush into this – take your time and you'll be rewarded.