Hit and run, parked car, 17 years old, consequences?

I hit a parked car the other day and didn't leave a note as I was panicked and didn't know what to do. My car axel was broken so I had to park it across the street from the car I hit. Then the day after, my car was towed in by the police and impounded. I then proceeded to turn myself into the police and gave them full details as to what happened. They told me to somehow get ahold of the person whose car I hit and get them not to prosecute by confessing to them and paying for the damages and maybe a little extra. Therefore, I left a note on their car telling them to call. Where do I go from here? I admit my mistake and am completely remorseful and mortified. I will never fail to leave a note ever again I'm just not sure as to what happens next. If they don't prosecute, will I still have to face court? Nothing was really explained to me in detail. Also, we are not sure if my car is even worth picking up due to the broken axel and it was really a piece even when we bought it. Oh and the car I hit was old and I didnt leave a dent just scratches. The police officers also told me that the owner was not going to even report the incident until they found my car across the street and it looked suspicious, as someone had broken one of the windows on my car...