Do past sins prevent the answering of future prayers?

If your past is filled with sins, you must wash them away with sincere repentance. If you repent with sincere repentance, then Allah Almighty will erase them from you and will not hold you accountable for them in this world or in the Hereafter. Indeed, the repentant person is not punished, neither by divine law nor by divine decree. Be at peace and supplicate to Allah with certainty of His response, knowing that nothing is impossible for Him, being content with what He decrees, and entrusting your affairs to Him.