I learned how to pray when I was a child, but without saying Takbeerat Al-Ihraam (saying 'Allaahu Akbar' while one is standing at the beginning of prayer). I did not know that it is one of the pillars of the prayer. What is the Sharee‘ah ruling on my past prayers? In a Hadeeth, the Prophet, sallallaahu ‘alayhi wa sallam, said: "My Ummah is forgiven for what they do out of mistake or forgetfulness."

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Takbeerat Al-Ihraam is one of the pillars of prayer and a prerequisite for its validity, according to the preponderant opinion of scholars. Since you were ignorant about that, you are not required to make up the prayers you performed without Takbeerat Al-Ihraam. In such a case, ignorance is the reason behind this ruling, not mistake or forgetfulness.

Ibn Taymiyyah said:

Whoever performed the prayer without tranquility as he was ignorant that it is obligatory, the scholars provided two known different opinions whether he is required to make up the prayer after the expiry of its time or not….The sound opinion is that he is not required to make up the prayer, as the Prophet, sallallaahu ‘alayhi wa sallam, said to the Bedouin who prayed incorrectly before him: "Go back and pray, for you have not prayed." When he had done that two or three times, the man said: "By the One Who sent you with the truth, I cannot do better than that. Teach me what makes my prayer valid." The Prophet, sallallaahu ‘alayhi wa sallam, then taught him how to pray tranquilly but did not command him to make up the prayers he had performed before that time. Although the man said, "By the One Who sent you with the truth, I cannot do better than that," the Prophet, sallallaahu ‘alayhi wa sallam, commanded him to repeat the present prayer only because its time had not expired. As for the past prayers, the Prophet, sallallaahu ‘alayhi wa sallam, did not command him to make up for them, although he abandoned some of the obligations of prayer.

Nonetheless, you are blameworthy because you neglected learning the prayer and its rulings. You are not excused for being ignorant about such rulings and you are guilty of negligence.