As prayer is simply having a conversation with God, anyone, absolutely anyone can pray. Of course, the type of relationship we have with God will determine how we go about praying, how often, and if we even desire to pray to Him. For instance, it would be difficult to pray to God if you did not believe He existed!
In a nutshell, God hears the prayers of saints and of sinners.
Saints – As God’s children – anyone who confesses that Jesus is Lord of their lives and Lord above all (saints here does not mean a selected few promoted to sainthood because of some good deed) – we have FULL access to approach God in prayer. Ref. Hebrews 4:16
Sinners – a sinner is anyone who still stands guilty and disgraced before God, not any any account of God Himself, but because that persons has refused to accepted redemption made available to him through the death, burial and resurrection of Jesus Christ. John 3:18 says Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son.
However, in man’s state of sinfulness, God has extending mercy to Him that if he should call on Him in a sincere plea of repentance, he will be heard. We see in 1 Kings 21:25-29 where even the wicked King Abab prayed for mercy… though sadly he still turned his back away from God. In Luke 7:36-50 we see a sinful woman begging for pardon. God will hear any sincere prayer of repentance because it is His will that none perish but that all come to repentance. Ref. 2 Peter 3:9
The elders of the Church – Like any relationship, several factors can put a strain on our ability, even willingness to communicate with God. Some of the reasons may include discouragement, sickness, a struggle with sin, hopelessness. In the times, we can seek out counsel and prayer from the leaders within our Church (or any church God may lead you to, for that matter). James 5:14-15 says Is anyone among you sick? Let them call the elders of the church to pray over them and anoint them with oil in the name of the Lord. And the prayer offered in faith will make the sick person well; the Lord will raise them up. If they have sinned, they will be forgiven.