Is Repentance Valid in Islam if Punishment Isn't Applied?
Question

I have a question that is confusing me. If a married or unmarried person commits the sin of immoral conduct, or major sins such as stealing, backbiting, riba, etc, and persists in doing that for a long time, then he comes to know Allah and he repents sincerely to Allah, seeking the Face of Allah, and he seeks the forgiveness of those about whom he gossiped, and returns what he stole, and gives up riba (usury) and all the sins that there are between him and Allah such as Zina, drinking, failing to pray etc, but the Hadd punishment is not carried out on him, will Allah accept his repentance and his worship, no matter how great his sins were? Or is it possible that Allah will not accept his repentance and his worship will be rejected? Will Allah save him from the torment of the grave and from Hell? What should he do in order to avoid punishment and so that Allah will be pleased with him?.
Praise be to Allah.The Mercy of Allah: Greater Than Any Sin
You should note that it is not permissible for a Muslim to think of the sins from which he has repented as being too great, for the mercy, pardon and forgiveness of Allah are greater than his sins.
Restoring Rights: A Condition for Valid Repentance
If the sins had to do with other people, then it is obligatory to restore people’s rights to them. If the sin has to do with something that is between a person and his Lord, then it is sufficient for him to repent, seek forgiveness, regret what he did and resolve not to go back to those sins. It is not a condition of repentance that the Hadd punishment be carried out on the repentant person. He should conceal himself with the concealment of Allah, Achieving sincere repentance is better than confessing so that the Hadd punishment may be carried out.
This person has repented well and has given back to people what is rightfully theirs, so he should not let the devil come and spoil his repentance.
It should be noted that Allah turns the bad deeds of the repentant into good deeds. Allah says (interpretation of the meaning):
{And those who invoke not any other Ilah (god) along with Allah, nor kill such a person as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace; Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allah will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful. And whosoever repents and does righteous good deeds; then verily, he repents towards Allah with true repentance.} [Al-Furqan 25:68-71]
When Hadd Punishments Must Be Carried Out
The offences which the sultan (Muslim ruler) hears of are the ones for which the Hudud punishments must be carried out. As for those of which he does not hear, then it is better to repent from them and to conceal oneself with the concealment of Allah.
The scholars of the Standing Committee said:
If the Shar`i ruler hears of offences and they are proven by sufficient evidence, then the Hadd punishments must be carried out, and it is not waived by repentance, according to scholarly consensus. The Ghamidi woman came to the Prophet (peace and blessings of Allah be upon him) asking him to carry out the Hadd punishment on her after she had repented, and he said concerning her: “She has repented in a manner that if the people of Madeenah were to repent in this way, it would be sufficient for them.” But despite that he carried out the Shar`i Hadd punishment on her. But no one has the right to do that but the sultan.
But if news of that offence does not reach the sultan, then the Muslim should conceal himself with the concealment of Allah and repent sincerely to Allah, so that Allah may accept his repentance. (End quote from Fatawa Al-Lajnah Ad-Da’imah, 22/15)
And they said – responding to one who wanted to carry out the Hadd punishment and who was not sure that repentance from Zina would be accepted –
If a person repents to his Lord sincerely, then Allah has promised that He will accept his repentance, and will compensate him with reward. This is by His kindness and generosity. Allah says (interpretation of the meaning):
{And those who invoke not any other Ilah (god) along with Allah, nor kill such a person as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace; Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allah will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful.}  [Al-Furqan 25:68-70]
The conditions of repentance include: giving up the sin, regretting what one has done and resolving not to go back to it. If the matter involves the rights of other people, then one must also ask them for forgiveness.
It was narrated from `Ubadah ibn As-Samit (may Allah be pleased with him) that when the women gave their oath of allegiance (Bay`ah) to the Prophet (peace and blessings of Allah be upon him), he said: “Whoever among you is faithful (to this oath), his reward will be with Allah. Whoever does any of these things (wrong actions) and is punished for it, that will be an expiation for him. Whoever does any of these things and Allah conceals him, then it is up to Allah: if He wills He will punish him and if He wills He will forgive him.”
The Prophet (peace and blessings of Allah be upon him) encouraged sincere repentance. In the story of Ma’iz (may Allah be pleased with him) he said: “Why did you not leave him alone, perhaps he would have repented and Allah would have accepted his repentance.” Malik narrated in Al-Muwatta’ from Zayd ibn Aslam (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “O people, the time has come for you stop transgressing the sacred limits set by Allah.  Whoever commits any of these evil actions, let him conceal himself with the concealment of Allah, for whoever discloses his actions, then we have to carry out the Hadd punishment (that is prescribed in) the Book of Allah.”
So you have to repent sincerely, offer prayers regularly in congregation and do a great deal of good deeds. (End quote from Fatawa Al-Lajnah Ad-Da’imah, 22/44-45)
For more details, please see the following answers:
Will Allah Forgive Me If I Repeat the Same Sin?
Persisting in sin
Acceptance of repentance
Sin and its Effects on the One Who Commits it
The punishment for zina and how to keep oneself from going back to it
How can someone who used to commit adultery and steal repent?
And Allah knows best.