90 Ski Nautique-electrical problem

I purchased the boat a year ago with work needed.  Upon purchase till current all 3 dash light stay on all the time (volts,temp, & oil).  Gauges are working fine and indicate good readings.  Sometimes when I turn the key nothing happens (silent not even the solenoid clicks nor any starter noise).  Both are new and all battery contact points have been cleaned.  Also key ignition switch was replaced.  I even shortened the positive battery cable which was 4 feet too long.  None of these new parts changed the symptoms.  Other times it starts right up.  It also appears the electrical issue is draining my battery.  I suspect the dash lights are connected with the intermittent starting problem.  Any suggestions?  Has anyone experienced this?  Thank you!