Am I qualified to be a police officer?

I currently have a associates degree in criminal justice. I have never been or arrested or even received a traffic violation ticket. I am in pretty good shape i run everyday and lift wieghts twice a week. My only flaw is that when i was a 18 I enlisted in the marines after high school in the hope of being able to defend my country. I was in the delayed entry program for six months and i loved every minute of it. I was excited about becoming a marine and it was my dream. After six months in the d.e.p the military called me up to return to physical examination for a second time to re exam my chest because my sternum was slightly sunk in but not really noticeable. After my inspection i was told that in two weeks i would find out if i was fit for duty. After those two weeks I was notified by my recruiter that my condition disqualified me from duty and the only way i could go to basic was if i signed a waiver. My father, who was a major in the army rangers said i should not sign it and go to college and try again later to join the service. If I could go back now i would have signed that wavier in a heartbeat but i was a guilable stupid kid who listened to everyone but myself. What im wondering is by me deserting my military dream will it show up on my record when i try to become a state trooper? And will it effect my chances of being a police officer? Thanks any info will be appreciated.