Sea Ray 2006 185 Sport has power but will not turn over

So, I bought this boat this past week and when I put it in the water it started right up although I did have to play with the gear shift to get it to turn over (I just shifted in and out of neutral and then it started right up.) It ran for 5 minutes or so and then just stalled. Same thing three times and then seemed to be fine although it was idling fairly high. So I took it out drove it at about 30 mph for 10 minutes and once I stopped and shifted to neutral it stalled again. This time no response to turning the key and no matter how many times i screwed around with the shifter nothing happens it doesn't even try to turn over. One of the guys on the dock thought it is either the starter or shift lever not recognizing it is in neutral?

This is my first boat and was actually my first day out on the water... Have to learn some how...