Geoff... with power issues, it's worth it to see if the voltage is still within spec when the unit is turned on. If there is too much resistance in the line, the application of a load will pull a normal-looking level down to something marginal. I'm not saying that's what it is, but it's a good first thing to check.
It does seem a bit strange, given the new board. My bet is that it's OK and that something local is amiss. Try unplugging the GPS
(NMEA) input and any other devices you may have... a ground loop can make a mess. If all else fails, try it "on the bench" with a known good power supply (direct from a car battery
or similar). I'm sure that's a bit of a pain since you probably have the power cable nicely installed, so try the in situ
experiments first. Can you get to the power at a point not too far from the unit? In a pinch, you can probe into insulation
with a pin or needle, clipping your multimeter to them securely... then seal it with goop to make sure they don't wick in salt water
Hopefully it will be something simple and that kick, well placed, might locate an intermittent connection!
One question: is the symptom you are seeing now the same as the one that prompted you to send it in for service
? (Man, $780... that is NUTS... even with falling US dollars. Did they tell you that the old one was actually defective?)