If spot checking a couple of things doesn't turn up the problem then you should do a methodical, step by step check.
DISCLAIMER!!!! Do not do this if you are not familiar with the proper safety
procedures for dealing with AC electricity. It is dangerous and can kill you, especially around boats and water.
First, do you have a good voltmeter and do you know how to use it? If no, may be time to call a pro and pay for the repair. If yes, then
1. Start at the shore power plug
on the dock and examine the socket for evidence of corrosion
. If it looks good then check for voltage. If voltage is OK then
2. Check your power cord both ends for corrosion
and evidence of heat damage. If it appears good then plug
in the dock side and check the boat side for voltage. If you see voltage there then
3. Check the boat plug for corrosion and heat damage. If that looks OK then
4. Turn off the power at the dock plug, connect your cord at the dock. Make sure the AC switch is turned off on your boat electric
panel and connect the boat side of the power cord. Turn on the dock power switch then go to the boat and make sure all AC circuits are turned off and turn on the main AC power switch. Does your panel have a meter built in? When you turn on the main AC switch does it show voltage? If yes then
5. Turn on the switch for the battery charger
and check to see if the batteries start getting charge. Also check the AC voltage meter on the panel to make sure it still shows voltage.
Try these and let us know what you see.