I think I see prayer as conversation. I've always found Brother Lawrence's 'Practise of the Presence of God' a really helpful model in both prayer and life - the idea that every moment, all that we do, is soaked in God's presence, and that we can be aware of that - through the mundane as well as the spectacular, through washing up as well as 'prayer time'.
For me faith in God is a relationship, and relationships are sustained through communication. I therefore witter away to God through my day. I like a seperate time to pray as well, as it helps me centre and get through the day, and I do also believe that God does intervene and does answer prayer - not always how we would think or hope. I think prayer is a spiritual discipline, but it can also be incredibly freeing to go through the day with the attitude that prayer is simply communication with the God I am in relationship with.
I do ask God for healing (have been chronically sick all my life) and will not give up asking, but also think that sometimes God doesn't heal. I have seen people healed, and have seen people not healed. I cannot pretend to understand, but I don't think God is the sort of God that heals someone if enough people pray or if a certain prayer is prayed. I think God sees where our heart is and our heart towards God - praying is simply voicing something of this.
It's listening too - it's conversation. I mostly don't 'hear' anything, certainly not audibly. But thoughts, impressions, bible verses may come to mind and it feels like God's communicating. The more I pray, the more this happens - communication is the key to relationship.
Don't know if that all makes any sense....hope you feel more able to pray soon, OP, and I do understand where you're coming from - have thought along the same lines. And also recommend the Philip Yancey book.