My first wife and I were married by the justice of the peace. I was baptized in a Baptist church, but she was not baptized at all. Do I have to go through an annulment process?
Since neither you nor your wife was Catholic when you got married, there were no special permissions or dispensations required of either of you. The Church, therefore, presumes your marriage to be valid. If you wish to attempt marriage again, you will first need to have your marriage investigated for nullity (i.e., get an annulment) to be certain that it was invalid. If it was, then you should be free to attempt marriage again.