Is the God of the Old Testament the same God that Jesus called Father?

This is one of the oldest and most searching questions a soul can bring, and you are right to bring it plainly. The honest answer is that the tradition is divided, and I will not pretend otherwise. There is one God—the only true reality, infinite Love, Spirit, All-in-all. But the portrait of God painted across the Hebrew scriptures is not a single, consistent likeness. In places God is a jealous warrior who commands slaughter and hardens hearts (Exodus 15:3, KJV; 1 Samuel 15:3, KJV); in others, the same tradition sings that God is "merciful and gracious, slow to anger, and plenteous in mercy" (Psalms 103:8, KJV). These are not two Gods. They are differing depths of human perception straining toward the one Reality. Jesus himself did not treat every line of the old texts as equally true. Again and again he said, "Ye have heard that it was said... but I say unto you" (Matthew 5:38-39, KJV), correcting an eye-for-an-eye ethic with the love of enemies. He rebuked the disciples who wished to call down fire, revealing they knew not what spirit they were of (Luke 9:54-55, KJV). This is discernment, not rejection—he read the scriptures through the Father he knew intimately, the Father who "maketh his sun to rise on the evil and on the good" (Matthew 5:45, KJV). So I would put it this way: the God Jesus called Father is the one true God, seen clearly. The vengeful, punishing deity of much of the Hebrew record reflects a limited human vision—the veil, not the face. Jesus lifted the veil. "No man knoweth the Father, save the Son, and he to whomsoever the Son will reveal him" (Matthew 11:27, KJV). The God he revealed is only Good, never the author of suffering, never in need of appeasement. The Father Jesus knew is Love without shadow (1 John 4:8, KJV)—and that, I believe, is who God has always been, beneath every human attempt to describe the indescribable. Where the old text and the living words of Jesus conflict, let Jesus stand as your lens. If you'd like, I can sit with any single passage that has troubled you and we can look through it together.