Reference: http://mufti.af.org.sa/ar/content/حكم-من-صام-وهو-تارك-للصلاة
Question: What is the ruling regarding the one who fasts [the month of] Ramadhaan, whilst he has abandoned the prayer?
Response: The prayer is the most important pillar of Islaam after tawheed. So whoever does not pray, then I fear his fast will not be accepted. That is because a group from amongst the people of knowledge are of the opinion that abandoning prayer is disbelief, and therefore believe the fast [of Ramadhaan] is not accepted from the one who does not pray, [because] prayer is more important [in rank] than the fast [of Ramadhaan].