Ramadaan fasting is not acceptable if one does not pray
Question

I fast Ramadaan but I do not pray. Is my fasting valid?
Praise be to Allah.The Ramadaan fast, and indeed any righteous deed, is not accepted if you do not pray. That is because not praying constitutes kufr as the Prophet (peace and blessings of Allaah be upon him) said: “Between a man and shirk and kufr there stands his giving up prayer.” Narrated by Muslim, 82. See also question no. 5208. 
No righteous deed is accepted from the kaafir, because Allaah says (interpretation of the meaning): 
“And We shall turn to whatever deeds they (disbelievers, polytheists, sinners) did, and We shall make such deeds as scattered floating particles of dust”
[al-Furqaan 25:23] 
“If you join others in worship with Allaah, (then) surely, (all) your deeds will be in vain, and you will certainly be among the losers”
[al-Zumar 39:65]
al-Bukhaari narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever forsakes ‘Asr prayer, his deeds are in vain.” (al-Bukhaari, 553). What is meant by “his deeds are in vain” means that they become invalid and will not avail him anything. 
This hadeeth indicates that in the case of one who does not pray, Allaah will not accept any deed from him, so the one who does not pray will not benefit at all from his deeds, and no good deeds of his will ascend to Allaah. 
Ibn al-Qayyim (may Allaah have mercy on him) said concerning the meaning of this hadeeth: “The apparent meaning of this hadeeth is that those who do not pray are of two types: those who do not pray at all, which renders all of their deeds invalid, and those who do not pray some days, which renders his deeds on that day invalid. So the loss of all good deeds happens to those who do not pray at all, and the loss of some deeds happens to those who miss some prayers.” From Kitaab al-Salaah, p. 65 
Our advice to the sister who asked this question is to repent to Allaah, to feel regret for her negligence in her duties towards Allaah for exposing herself to His wrath, anger and punishment. Allaah accepts the repentance of those among His slaves who repent to Him, and forgives their sins; indeed, He rejoices greatly at that. The Prophet (peace and blessings of Allaah be upon him) has given glad tidings to those who repent when he said: “The one who repents from sin is like one who did not sin at all.” Narrated by Ibn Maajah, 4250; classed as hasan by al-Albaani in Saheeh Ibn Maajah, 3424. 
So she should hasten to do ghusl and pray, so that she may become pure both inwardly and outwardly. She should not delay repentance and say, “I will repent tomorrow or after tomorrow, because she does not know when death will come. She should repent to Allaah before regret will be of no avail. 
“And (remember) the Day when the Zaalim (wrongdoer, oppressor, polytheist) will bite at his hands, he will say: ‘Oh! Would that I had taken a path with the Messenger (Muhammad).
Ah! Woe to me! Would that I had never taken so-and-so as a Khaleel (an intimate friend)!
He indeed led me astray from the Reminder (this Qur’aan) after it had come to me. And Shaytaan (Satan) is to man ever a deserter in the hour of need’”
[al-Furqaan 25:27-29 – interpretation of the meaning].