Oooh this is deep stuff, and very close to the bone.
My personal take on it is this: Yes I can feel God with me, very often. I became a christian as a teenager and remember very well the 'before' and 'after'. My life changed radically. Who I was changed radically, and for the infinitely better. It was like, I'd been trying to be the best person I could, which was frustrating and so disappointing. Then when I became a christian the whole perpective changed - I didn't have to try any more because God in me was being the strength that I needed to be the person I could never be on my own. I felt peace, purpose, I felt that there was order to the world, I felt known and loved by God, I felt that I could question and scream and cry at Him but He'd never stop loving me and knowing me through and through. And over the years I have questioned and screamed and cried at God but I still feel that His love goes on forever.
So,yes, there are unanswered prayers - or at least prayers which I haven't seen the answers to (and by faith I think there is a difference). Although there are answered prayers too. As time's gone by I'm thinking more and more that God calls us to be "his hands and feet" - i.e. in praying for healing, we need to be praying for all doctors, nurses and others who care physically. In praying for the lonely, we need to get off our backsides and knock on our neighbours' doors or whatever. In praying for the homeless, we get involved in whatever way we can, we do our best to help those at the margins of society. If we aren't willing to do these things, our prayers and our faith are a bit limited. So praying for miracles (i.e. things happening that are outside of the normal course of things) is only part of what christinaity is about - it's also about being willing to be part of the answer to your own prayers.
IME people aren't that impressed by miracles. It is so easy to explain them away if you want to. It is much harder to explain away why people give their lives to helping the poor, the homeless, the needy. I honestly believe that if christinas did what they talk about more, we'd have a lot more credibility in the world.
And it makes my heart ache just thinking about it.