The answer is entirely contingent upon whether you set specific times and plans, or whether you asked her to "go out together some time". If she agreed to have lunch/dinner/whatever with you at x time and date, then she wants to go. The date could still go abysmally, but she wouldn't agree to specific plans and then try to get out of it. So, odds are she wanted to go out with you and you're fine (at least for now).
If, on the other hand, you said "go out together some time" or something similarly vague, you could be in trouble. First of all, it was a mistake to leave it at that. If she was really into you, after you said that she would have pushed for specifics, e.g. "how's this Thursday?" If she was neutral about it, after she tentatively agreed to go out with you then the ball was in your court to say "do you have dinner plans Thursday?"
But that's all in the past. Now, assuming you didn't set specific plans (which I think is a safe bet), what you need to do is try to casually "run into" her some time. I don't know the logistics of your job and office, so I'm not sure how you would go about that, but figure it out. You cannot go the rest of your career avoiding her, it's ridiculous. And, if you play this with supreme confidence, you still have a chance to win her over. So you casually walk past her desk, or whatever. This will not be easy to pull off but you can do it.
1. DO NOT show up sweaty, nervous and/or stammering. This must not seem rehearsed, either. You have to approach this casually. Do not make it awkward. Make it okay, which it is.
2. Give her a charming smile and say "What's up?" (this phrase implies a casual confidence, it is important that you use it). Say, "Hey, I haven't seen you after work lately. Look, no hard feelings if you don't want to go out, okay? I don't want to mess with your schedule." Give another winning smile, wish her a good weekend or evening, and walk away.
3. DO NOT engage in a long heart-to-heart about your feelings, your sick parent, her feelings, or anything of the sort. This is a short and sweet exchange.
4. DO NOT say anything to the effect of "we can still be friends". The word friends should not come out of your mouth.
5. When you see her again, laugh and joke along with the rest of the group, subtly include her in the conversation.