Thank you for your question. I understand this situation must be hard for you since you seem to really like this girl. In the end, it will be up to you to decide what you really want to do, but I can certainly give you some things to think about before making your decision, whether or not you try to win her over.
Sometimes people do not always say what really is on their mind (for example they might be trying to protect themselves or the other person). In fact, she did not say that you had no chances at all when you asked her that question, so this may indicate that she has some feelings for you, though they are not strong enough to make her see you as more than a friend.
On the other hand, as a friend we have to respect others and that include respecting others’ feelings and choices, such as the fact that right now, she sees you only as a friend.
Feelings and relationships are something that is personal to everyone and nobody can tell you what to do or not to do, even in this case. You have to figure it out by yourself and trust your instinct on what decision is the best for you. Sometimes perseverance is worth it, but sometimes it can be dangerous to a friendship. Are you willing to lose her friendship if this does not work out? On the other hand, maybe you should take some distance from her at this point, to try to figure out what you truly want from this relationship. It is hard to always be in contact with someone who may not share your feelings and who may be sending ambiguous messages. What does she get from your relationship? Is it just the attention? Or is there a potential for more? Do you have any chances at all with her? You may want to ask her those questions as well.
The most important thing to keep in mind is that you deserve to be with someone who truly cares and loves you. If you decide to persevere with this person and she does not respond to your feelings, do not stay for too long in a situation which might be hurtful for you in the end. In general, people tend to become more attached to others with time, and it might become harder for you to get away from the situation.
I hope this helped you somewhat in making your decision. Feel free to ask again if you have any other questions!
Karine, for AlterHeroes