The Existence of God and my Experience

Is it possible to convince someone of the existence of God if they are already predisposed to doubt?
This question has begun to haunt me recently as I've been doing some studying. I've been reading two book simultaneously; Christian Theology, An Introduction to Its Traditions and Tasks edited by Peter C. Hodgson and Robert H. King, and Essentials of Christian Theology Edited by William C Placher. I like to review the basics of theology occasionally. I learned some French in High School, but didn't keep up with it and so its gone. So I review the basics of theology now and again to stay 'sharp'. In 'Essentials' an essay is included by John B. Cobb Jr. entitled 'Does it make sense to talk about God' in which we addresses some of the doubt and skepticism regarding a belief in God in our age. Interestingly enough I have been encountering this same skepticism recently. Cobb addresses the skepticism of those who trust only in experience in order to believe. Since they have not experienced God in a direct way, the idea of God cannot be accepted or trusted. Cobb makes an astute but simple argument to this skepticism by showing the logical progression of this line of thinking. If we can only trust in that we have directly experienced, then history does not exist.
Since I did not meet George Washington, I should be skeptical of his existence. Since I did not witness the Holocaust with my own two eyes I should be skeptical of its reality, and so on. (Cobb doesn't say that specifically, that is my example, and I don't believe it... this is just an example. Just to explain, there are photographs from WWII but not of Jesus... yes, but photographs can be faked. When I explain my trust in the Biblical witness this is the nature of the argument... it could have been faked. A fanciful myth that I cannot trust. Could we not wonder this about a number of things? including our own birth-certificates?) Personal experience, he posits, cannot be the sole authority for belief since it would mean that history would no longer have any bearing on our present or future.
I think he makes an excellent argument. But I wonder if it would hold any influence 'on the ground' so to speak. I could offer that argument to those skeptics that I have met recently, but I wonder if they would find that argument compelling.
So my questions are...
is a sound theological or philosophical argument for the existence of God compelling? If not, what will be?
given Cobb's argument re: Experience, isn't the Bible a collection of personal experiences of the living God? So isn't the Bible itself built upon experience and the telling and re-telling of personal experiences?
Should there be room in church for skeptics... people who have doubts about the existence of God or the divinity of Christ? How do we make that room for those who are seeking or open, but still doubtful... or for those who are comfortable doubting frankly, but who want to be a part of a community of integrity, honest, compassion and generosity?
My next few posts will follow this line of consideration and I look forward to your input.