What is the ruling on the prayer of one who led the congregational prayer but did not raise his hands during the opening takbir and his voice was not heard with the takbir, rather he immediately recited Al-Fatiha aloud?

Raising the hands at the opening takbir (Allahu Akbar) is a Sunnah according to the majority of scholars. Following someone who does not raise their hands at the opening takbir is valid. The imam not vocalizing the takbir does not affect the validity of the prayer. If you doubt that he did not utter the opening takbir at all, the default assumption is the validity of a Muslim's prayer, so do not pay attention to the doubt. However, if you are certain that he did not utter it, then the prayer must be repeated, because whoever omits the opening takbir has not had their prayer validly commenced.