Contradiction with Proverbs 28:9
While Psalms 27:7 speaks of God hearing when called upon, Proverbs 28:9 indicates that if one turns away from God's law, their prayers become an abomination.
Proverbs 28:9: He that turneth away his ear from hearing the law, even his prayer [shall be] abomination.
Contradiction with Isaiah 1:15
Contradicts the plea for God to hear in Psalms 27:7 by stating that even if many prayers are made, if one's hands are full of blood (sin), God will not listen.
Isaiah 1:15: And when ye spread forth your hands, I will hide mine eyes from you: yea, when ye make many prayers, I will not hear: your hands are full of blood. [make...: Heb. multiply prayer] [blood: Heb. bloods]
Contradiction with Micah 3:4
Psalms 27:7 is about asking God to respond, whereas Micah 3:4 notes that people will cry out to the Lord, but He will not hear them because of their evil deeds.
Micah 3:4: Then shall they cry unto the LORD, but he will not hear them: he will even hide his face from them at that time, as they have behaved themselves ill in their doings.
Contradiction with James 4:3
In contrast to the plea for God's response in Psalms 27:7, this verse says prayers may not be answered when asked with wrong motives.
James 4:3: Ye ask, and receive not, because ye ask amiss, that ye may consume [it] upon your lusts. [lusts: or, pleasures]