Walt wrote:
Check, clean and torque all the batt leads first.. these are the most common culprit. Next, the engine ground, followed by the helm pos and neg leads. If that doesn't do it, keep on going!
To add to Walt's excellent advice, REMOVE each connection to check and clean it. Don't just give it a visual once-over or just re-tighten a clamp. Lots of times a corrosion problem isn't visible, it's only by taking the connection off the post (or wherever) that you might see problem.
Also, get a voltmeter (radio shaft sells 'em cheap) and check the DC voltages. Check it at the battery without anything connected to it. Then connect the main cables, make sure everything's off and check it again at the battery. The voltage should not drop much. If it does then something that got reconnected it drawing too much power. Next, start checking the 12vdc positive at the various devices that aren't working properly. There should, again, not be much of a voltage drop. If there is then there's an issue with the wiring going from the battery to that device.
When the engine is running you should see voltage between 13 and 14 volts. Anything above 15 or below 12 and you've got a problem with the alternator charging circuit. Same thing if you've got a shore power hookup and a battery charger on board. When there's no charging going on you should see 12 or slightly more. As the battery drains the voltage will drop. Try to avoid ever letting the battery get drained below 10 as that greatly reduces the life of it.