Mithadon,
Have you ever considered that God might not be limited to the currently accepted modes of thought? Why should He adapt to us? God has described the path to wisdom - the path to knowledge about Him, and it is by including Him in your reality.
Let me make an extreme example: Say you were exceptionally rational and honest: a good man with good principles - but that living this way meant that you only accepted what you saw in your immediate presence as real. Nothing outside what you could experience and verify with all five your senses exists or can change your life. You are also living in a small wooden house in the middle of nowhere.
By your own decisions, you choose to exclude any possibility of God from your life. You say you invite God in, but at the same time you make yourself into a little ball, cup your hands, and say: this is where I want Him to be.
On the other hand, if you believe that God can and wants to enter our life, you must be open to any possibility of who God might be, what He could do - and be prepared for the possibility that it might not be within your current sphere of reasoning. Of course God can intrude, shake things up a bit, make you wonder... but will you acknowledge that it was Him, or was it just hormones? Remember: nothing - nothing - can encompass more than denial.
My personal experience is that knowledge of God exists within the parameters of doing what God wants you to do. Nothing is automatically excluded or automatically included. You say God should prove himself to you...
What if He already has? Would you see it? Would you accept it? I'm not talking photographs of apparitions, miraculous events in your life, or sudden enlightenment - these are all things that suppose God cannot do something that is simply what it is - that He is not simply "who He is". If you can't experience God in your ordinary life, it means He is limited to "extra-ordinary" experiences. What do you think?