I hate being percieved as mean but sometimes i just need to be. This girl is either a huge attention seeker (for gunning your every attempt down just like that) or has some deeply personal problems that she will not spill out to the first, best person asking her whats up. In my honest opinion you should approach this girl without having in mind her troubled energy/looks. Imagine if you looked sad and everyone asked what was wrong, wouldnt they just enforce your current state of mind?
Offer her an alternative, be genuine, causal and fun to be around. No flowers or teddybears, that might scare her off if she's already that quite. How did she respond to you before she became the sad lady?
The first step to fixing broken relationships is to accept that they have ended - getyourextowantyouback.org