Can one who was born a Muslim and whose heart God has sealed against transgression touch the Qur'an or enter the mosque with the intention of repentance?

Allah accepts repentance from His servants and rejoices in it, and He forgives all sins, no matter how heinous or numerous, provided that the conditions of repentance are met: regret, abstaining from the sin, and not returning to it. The repentant person must increase seeking forgiveness, performing good deeds, and striving against the self to stay away from sins, and abandon despair and hopelessness in Allah's mercy. The hearts of the servants are in Allah's hands; He turns them as He wills. What Satan whispers about "sealing the heart" is to turn people away from the path of Allah. It is permissible to enter the mosque if one is not in a state of ritual impurity (janabah), and to touch the Qur'an if one is in a state of ritual purity (tahara).