Let us suppose someone is worshipping Allah but his intention when praying is not that may Allah save him from the hellfire and enter him into the paradise. His intention is that if I worship Allah he will be with me and help me in all the problems of my life. Then will he get the reward of his deeds on the Day of Judgment. Or what if someone prays to Allah to get closer to him?
Whether we worship the Almighty to get close to Him, or to get His help or to go to his promised paradise the fact of the matter is that we are worshipping Him because He is worthy of being worshipped. Therefore in principle it does not matter which of His particular blessings we are aiming for when we are worshipping Him. An honest act of worship will be accepted by the Almighty regardless.
However, there is no doubt that the better and purer a person is, the more he feels that he needs to worship God not only for rewards in this world or the hereafter and not to merely avoid His punishments, but out of love and respect that a servant has for his unique Lord.