What is the ruling on marrying a woman who ran away from her family, and it became apparent on the wedding night that she was not a virgin, then she became pregnant and gave birth to a full-term child seven months after the marriage, and the child was abandoned by being placed at the hospital gate, then the marriage contract was renewed with a new dowry and in secret?

The fact that a girl is not a virgin does not mean she is corrupt or has committed fornication, because the loss of virginity can occur for reasons other than intercourse, as Sheikh Ibn Uthaymeen stated.

As for the birth of a full-term baby in less than seven months, it does not mean that he is a child of fornication. Rather, he is your son and attributed to you, based on the Prophet Muhammad's (peace be upon him) saying: "The child is for the bed (i.e., the husband)," and the minimum period of pregnancy is six months. If it is proven that he is your child, you have no right to deny him except through li'an (oath of condemnation).

What you and your wife's brother did by placing the newborn at the hospital door is a great wrongdoing and exposes him to destruction. You both must repent sincerely. Since he is your son, it is your duty to search for him, care for him, and spend on him, for the Prophet (peace be upon him) said: "Indeed, Allah will question every guardian about what he was entrusted with."

Your thinking about renewing the marriage contract is based on considering her an adulteress, which is incorrect, because the loss of virginity does not necessitate fornication. You must not surrender to the whispers of Satan.