Starting issue

Hello, I have an issue with the car. The car will sometimes start just fine, and then a few minutes or hours later it will not start. All lights on the dash light up; everything powers on. When the key is turned to crank the car, there is no sound, but all lights remain on. I turn it off, and try again, repeating about five or more times. Then, it will slowly turn (slow wind) then faster winding, then it will eventually turn over and start. This keeps happening daily. As I stated, sometimes it starts fine, and then it does this. Battery seems good, looks slightly new. Starter perhaps?
It runs great when it is started, it just goes through this cycle before it will run.

I also forgot to mention that whenever this happens, I notice that the clock on the stereo resets to 12:00. Maybe this will help out as a clue.