Was the marriage invalid due to the absence of a contract, considering that it took place without documented proof, in the presence of two witnesses and the woman's guardian, without the payment of the dowry, and was then followed by a threefold divorce?

The aforementioned marriage is valid if it fulfills the conditions and is free of impediments. Its non-registration with official departments affects only documentation and rights. If you have consummated the marriage with the wife, you owe her the full mahr, and she has become irrevocably divorced from you (a major divorce), and she is not lawful for you until she marries another husband and he consummates the marriage with her. However, if you have not consummated the marriage with her, she is entitled to half the mahr, unless she or her guardian waives it. You are not permitted to marry her again until she marries another man and he consummates the marriage with her, and then he divorces her.