Any suggestions as to what I have to do to make this work?

Get a 12v DVD player. It's the inverter causing you the trouble. I'm not
at all confident that you'll be able to effectively eliminate it on the
boat. I've got a 12v player in our 348 Vista and it's great. I actually
use the AUX-in on the DVD player to daisy chain input from an iPod.

That and you're likely to get better battery life using a 12v player anyway.
But if the player already uses an external power supply you may be able to
use a DC-to-DC transformer to adapt to whatever voltage it needs. But if
you want to just cut to the chase and get things working I'd dump the
AC/inverter setup and just get a player designed for auto/rv/marine use.

-Bill Kearney