Answer:
When Jesus was asked about the most important thing to do in life, he repeated the Old Testament number one commandment: that we love God with all our heart, soul, mind and strength. Which means it's not less love to think on the question of God because it's not an emotional thing done with our hearts. We can train our minds on evidence and facts and logic and reason and this pleases God. This is a way of loving God.
You sound as if your head and heart are at war with each other. If you tend to overthink things, it might be helpful to sit down with a piece of paper and write down all the intellectual obstacles that you have to not believing in God. Why can't you love God with all your mind? On the surface, it would seem it's because your mind has come upon facts and evidence that suggest that God cannot exist. What are those facts and evidence? Write them out.
Often when we boil down our intellectual objections, we find they don't hold water. Or we find a healthy dose of emotional/heart objection along with it... like for example, if I've been let down by a significant person - especially a Christian in my life. No actual evidence has been produced that militates against God's existence, but I'm now caught in an emotional blitz on my faith because I'm wounded. If i get outside the wounds, my brain may come up with the following problem: shouldn't Christians all be better people than everyone else if their Gospel is true? And if so, then this Christian who hurt me is fresh evidence that their Gospel is not true.
There's a certain logic to that, but as you can probably already tell, it's not an air tight case against belief in God. What I'm suggesting is that you discipline your mind to weed through it's objections to find the nut of the issue. Then investigate that with as much intellectual honesty as you can, seeking wise outside thinkers and i believe you'll find your reasons for God. Jesus said, "ask, seek and knock. For the one who asks, receives, the one who seeks finds and the one who knocks, the door will be opened." Just make sure as you seek you fulfill this important qualifier on your seeking: "with all your heart." (Deut 4:29) In other words, if you stop short because of personal pain or intellectual dishonesty or laziness, that's not seeking with all your heart and you can guarantee you'll find what you want to find rather than what's true.
Without knowing exactly which obstacles your mind can't get over, which your heart apparently CAN get over, i can only be general. But I'll direct you to two excellent resources that will present answers that may satisfy both your heart and your mind. The books I've found most helpful are CS Lewis' "Mere Christianity" and the much more recent book by Dr Timothy Keller, "Reason for God." Both I think are thorough, honest, and powerful arguments that any hungry mind can latch onto. Also some Q and A's on this Website may address concerns you have and you can submit a follow up for any area I haven't covered. Those two books will certainly address the most common and strongest objections to faith. They may allow your brain to unleash the restrictions you put on your heart by giving satisfying reasons, rationale, and logic to what your heart already suspects is true.
No one's mind is always completely satisfied with the evidence because God has clearly left enough of himself OUT of the world to make belief in him optional. Non-compulsory. This is in keeping with the Christian belief that God's prime desire for the human race is love response. And love can never be coersed.
Also, no one's mind and heart are always on the same page, so don't be too disturbed that yours are not right now. The situation in this brain/heart duality does not always have the mind left wanting either. I may find myself quite convinced based on the evidence that God exists, while my heart is reacting to emotional or circumstantial moods that come over me making God seem very unreal indeed. For you, right now, it's your mind that cannot join your heart in God belief. So don't overthink things... just THINK. That is, seek thoroughly and honestly and get wise insight from others rather than become myopically wound around your own doubts.
If you do, eventually an untroubled mind may join your heart in it's primal intuition and suspicion that God IS real.