1989 Bayliner 16', First Boat!

The problem does not occur all the time but if I shut my engine off
and then try to restart it after being out on the water it will not
turn over. During this time none of my gauges take any kind of
measurement but my trim on my throttle will still work so I know it is
not the battery. I think it is either a bad starter or a lose
conection wire from the throttle to the dash-board.

Any ideas that might help, thank you in advance.