The underlying assumption is that one believes in God because there is evidence for God.
Is it reasonable to believe in God if one does not like God?
Not necessarily, in my opinion.
Is it reasonable to believe in God because one fears God?
Same answer as above.
Is it reasonable to serve God out of duty if one does not like God?
Same answer as above.
What do you think? Are any of these reasonable?
If you think they are reasonable, why do you think so?
If you think they are unreasonable, why do you think so?
The simple (and reasonable) answer as to why I believe in God is because God is relevant in my life.
The relevance of God in my life rests not so much on evidence of God's existence as it rests on observance of the teachings of my faith -- a faith in which generations of very human sages have passed down their wisdom and contributions through their interpretation of Torah.
In regard to your questions: What I like is my synagogue, which provides comfort in difficult times. What I fear is not being as kind to others as I hope to be. What I serve out of duty are the mitzvot that apply to me.