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Chip, I would recommend that you get Nigel Calder's book "Boat owner's Mechanical and Electrical Manual" and do some study.
If (as you implied) you got a 6 volt reading on your batteries then they have been very deeply discharged and may not be recoverable. However there are threads on this and the "Cruiser's Forum" that should help you determine whether or not the batteries have been damaged beyond recovery. Batteries can be damaged very quickly by deeply discharging them or by overcharging.
2 group 31 batteries are marginal for refrigeration even if that is all you are using them for, but you are now trying to use that power for other things and are having trouble. What is the current draw for your 350 watt inverter when you are running your laptop? What else do you use your batteries for? Lights? What kind and how much power do they use? Do you anchor out? What is the power requirement for your anchor light?
You can not recharge a 50% discharged battery bank in 1 hour of engine running. There are other threads here and the Cruiser's forum that will help you understand the nature of battery charging.
What type of shore power battery charger do you have and what is it's capacity? Is it a 3 stage charger?
Lots to learn. Good luck.
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