Praise be to Allah.

In the answers to questions no. 5208 and 9400 we stated that not praying constitutes kufr that puts one beyond the pale of Islam. Based on that, any good deed done by one who does not pray will not benefit him and will not be accepted from him. 

Shaykh Saalih al-Fawzaan (may Allah preserve him) said: 

With regard to fasting when one does not pray, it is of no value or benefit, and it is not valid if one does not pray. No matter what other acts of obedience a person may do, they will not benefit him so long as he does not pray, because the one who does not pray is a kaafir, and the good deeds of the kaafir are not accepted from him. So there is no benefit in fasting if one does not pray. End quote. 

Al-Muntaqa min Fataawa al-Fawzaan (39/16) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

If a person fasts but does not pray, no fasting will be accepted from him, because he is a kaafir and an apostate, and no zakaah, charity or any other righteous deeds will be accepted from him, because Allah, may He be exalted, says (interpretation of the meaning):

“And nothing prevents their contributions from being accepted from them except that they disbelieved in Allah and in His Messenger (Muhammad (blessings and peace of Allah be upon him)); and that they came not to As-Salat (the prayer) except in a lazy state; and that they offer not contributions but unwillingly”

[at-Tawbah 9:54]. 

If their contributions – which refers to benefitting others – are not accepted from the disbelievers, then it is more appropriate that acts of worship, the benefit which is limited only to the doer, should not be accepted either. Based on that, the one who fasts but does not pray is a kaafir, Allah forbid, and his fasting is invalid. Likewise, none of his righteous deeds will be accepted from him. End quote.

Fataawa Noor ‘ala ad-Darb by Ibn ‘Uthaymeen (124/32). 

If the one who does not pray wants to offer an udhiyah, then he has to repent to Allah, first of all, for not praying. If he does not do that, and he persists in his ways, then he will not be rewarded for that sacrifice and it will not be accepted from him. If he does the slaughtering himself, then it comes under the heading of maytah (“dead meat”, from an animal that was found dead) and it is not permissible to eat from it, because meat slaughtered by an apostate comes under the heading of maytah and is haraam. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

If a man who does not pray slaughters an animal, that meat cannot be eaten. Why? Because it is haraam. But if a Jew or a Christian slaughters an animal, that meat is permissible for us to eat. So the meat slaughtered by (the one who does not pray) – Allah forbid – is more unclean than meat slaughtered by the Jews and Christians.

End quote from Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen (12/45) 

And Allah knows best.