I think a small part of the answer might be in how Jesus taught His disciples to pray. He began with, "Our Father, who art in heaven, hallowed be Thy name." I feel more connected to God in prayer when I start with slowing myself down, remembering that God is ruler of angels and ministering angels, gloriously enthroned far above in a scene that is powerful but I can't even imagine. He made a way through His Son Jesus Christ that all who call on His name may be saved. Sometimes beginning prayer with genuine gratitude is a good practice when the first doesn't work.
Discussion
I agree. Prayer starts with recognizing God for who He is, ourselves for who we are, and offering gratitude and prayer to our Creator.
So then how do we introduce that idea to people who, maybe on their childhood or teen years, tried to do just that, and gave up because it didn't seem to be "working"?
Maybe there's other church practices that help them? I get nothing from corporate worship (in the form of singing) most of the time, but occasionally I still feel like God drops a thought there for me in the midst of it.
I don't think we need to go quite to sin blocking the communication channels either. My most powerful prayers that I felt as though God prayed with me, were for others in situations that I know God cares about but I was powerless. I learnt about those situations because I was actively involved in ministry. We are in a war for our souls and contending for the souls of others. Prayer is a battlefield walkie-talkie we can't expect much of we use it to ask for a comfy bed and a pizza to be delivered.