Praise be to Allah.
Praying without having purified oneself is a major sin, and is one of the things for which a sinner will be punished in his grave. Al-Tahhaawi narrated in Mushkil al-Athaar from ‘Abd-Allaah ibn Mas’ood that the Prophet (peace and blessings of Allaah be upon him) said: “It was ordered that one of the slaves of Allaah be given one hundred lashes in his grave, but he kept asking Allaah and pleading until it was made one, and his grave was filled with fire. When it was lifted from him, he woke up and said: ‘Why did you whip me?’ They said: ‘You offered a prayer without having purified yourself, and you passed by one who was being wronged and you did not help him.’” Classed as hasan by al-Albaani in Saheeh al-Targheeb, 2234.
Your feeling regret for that is repentance, but does your repentance also require you to make up those prayers or not? This is a matter concerning which the scholars differed. It seems that you do not have to make them up, because prayer is an act of worship that is connected to a specific time, and if a person fails to do it at the specified time, then it is not valid, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever does an action that is not in accordance with this matter of ours will have it rejected.” Narrated by al-Bukhaari, 2697; Muslim, 1718. Your praying without having purified yourself is like your not having prayed at all, because a prayer offered without being pure is not valid.
We have stated in the answer to question no. 13664 that the scholars differed concerning the ruling on one who does not pray until the time for the prayer is over, without any excuse – does he have to make it up or not? So what you have to do is:
Repent from this great sin, and resolve not to return to it. And you have to offer a lot of naafil prayers, for “good deeds erase bad deeds.”
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said in al-Ikhtiyaaraat (p. 34): It is not prescribed for the one who deliberately does not pray to make up the prayers, and they are not valid if he does them. Rather he should offer a lot of voluntary prayers. This is the view of a number of the salaf. End quote.
And Allaah knows best.