Didn't have an intervening device, regardless...

I assume that there's a separate breaker for the computer than for the radar? In any event, if you want to check it you could do one (or all) of the following little tests:

Measure the voltage during the start-ups on the radar and computer circuits to see if you're getting good votage through the units (that won't measure amperage, but it should be instructive);
Try the start-up proceedure while the batteries are being charged by a robust outside source (the engine at 1800 rpm or a shorepower charger);
Put an independant 12v source temparily on the radar unit and/or computer from the battery;

I just doubt that the radar unit would function if didn't have adequate voltage for the NMEA sentences to be reported-out;

It is possible that you have a bad connection, of course. I just doubt that the sequence of start-up is related in this case.

(I know that the motor "start-up" loads of the radar transmitter makes a difference. But after it's running, it's running. If that were the issue, then after the start-up, why wouldn't the unit "show" from the NMEA interface unless it was an issue with the interface itself?)