Very good question sall
Allah forgives his rights except for sharing partners with him. SO if someone is neglectful of prayers or fasting or Zakat etc., Allah may forgive those sins upon repentence. Mind that these forms of worship are prescribed to shield one from from other sins and raise their level of taqwa.
Now lets move on!
Allah is just and will not allow any injustice on the day of justice (promise of Allah in Quran).
For crime against humans, there are punishments in Islamic law for people to receive punishment in the Dunya for their sin in the world, like for musder, stealing, slandering, false witnessing etc. for a greater good of the society. Allah SWT sayas in Suratul Baqarah: And there is life for you in Al-Qisas O men of understanding, that you may acquire Taqwa."
For one who didn't get justice in this life will get after it. There is no pardon for preying upon people without the consent of the agrieved.
So you find that there no punishments for not believing in Allah, prophet...., not praying, not fasting etc. because it relates to Allah only. For societal crimes, punishments are prescribed or pardon from the affected party.
Does it answer your question Sall?
yeah 
