Luckily the starting circuit on any boat is very simple. Here goes:
From experience, the problem usually lies at the battery itself. Make sure the voltage is high, and more importantly, stays high when you press the starter button. If the voltage drops, the solenoid won't have enough voltage to actually engage. Loss of voltage could be due to one of many problems – most likely the battery.
Next, you want to look the connections themselves. Check to see if the fuse holder on point 2 or the starter solenoid positive relay (which is a blade connector) is loose on point.
Lastly, the universal engines came with wiring harness with trailer hitch-style service disconnect, which is not ideal. As such, Catalina has issued a service call (years ago) to have those changed at both the engine and panel side.