Praise be to Allah.
Firstly, we would like to thank you for your question. Secondly, before we discuss the matter of your right to the mahr or dowry, we should discuss the matter of marriage itself. A Muslim man is permitted to marry a chaste woman from the People of the Book (see Question #689 and #2527), and she is judged according to her situation at the time of marriage: has she given up her former promiscuous, immoral ways or not? If she is chaste and pure, it is permissible for him to enter into a marriage contract with her, and in this case, the dowry is her undeniable right. In order to resolve the problem once and for all, we advise you to enter Islam, because Islam cancels out all previous sins and wrong deeds, so save yourself from the Fire of Hell and earn happiness in this world and the next. Once you have become Muslim there will be no element of doubt whatsoever concerning the validity of your marriage, and the problem to which you refer in your question will no longer be an issue at all. We ask Allaah to guide you and us, and to give you help and success. Peace be upon those who follow true guidance.