Star is right. Go talk to her in person, don't do any more emails. Tell her your situation and see if there is anything you can do to resolve it. If she says no go, that there is nothing she or you can do, then make sure that all your tests were graded properly and that no math errors exist. You may have to go over each test by hand. This is your right as a student. It is also your right to make sure all points were recorded properly in her gradebook. You'd hate to fail a class (or even worse, fail and not attempt to follow up on it) not because of something you did or did not do, but because of math error on the teacher's part.
As for going to the dean, if you stand a chance to lose financial gains, then you have everything to lose by not trying. First you will probably have to do the chain of command thing. I advise that you do that properly. Nothing makes a department head madder than to find out you went above their head BEFORE coming to them. Go to teacher, go to department head, go to dean of the division, go to dean of school, or however the chain goes. If you're still not happy, then you might be able to undergo an academic review which is kind of like a court case where you present your side and why you deserve consideration. Schools do this to show that they try and be fair, so an academic review is the last resort. Worst case, they can all say no. Best case is that they might MIGHT advise the teacher to pass you but only if you have a good track record of classes, attendance in that class and attempted extra credit (if it exists).
I personally don't think the lawsuit thing would work unless you have been graded unfairly or some sort of inequality exists otherwise.