Farzam... Without getting technical:
Do you have a battery switch on the boat that says 1-2-Both-Off???
If so...you have one "House" battery for things like lights and GPS and one Starting battery. With the switch...you can combine them or isolate them and my advice would be to isolate them so you never run the risk of not being able to start the boat! Any additional batteries you buy should be added to the "house" side to add more capacity to run different things.
The first thing you need to do is determine what type of batteries you have and whether or not they are any good. I assume you have a battery charge on board...so just put your battery switch on both and turn the charger on while you are plugged in at the dock overnight. In the morning...shut off EVERYTHING on the boat and wait an hour...then test the batteries with a volt meter. You should see 12.6-12.8V. If not...chances are you need new batteries...but there are a couple of other tests to make...but we'll save those till you do the above. Also..clean off the labels and tell us what kind you have...Group27, 8D etc. or failing that...the measurements of the batteries. Also do the batteries have water caps? If so...check the water level in each cell and if the plates are exposed...add DISTILLED water and hope for the best!
Finally...your hope of runing a microwave off the batteries will require a LARGE marine inverter AND a large bank of batteries. A 600 watt little microwave uses about 50 DC amps + conversion loss so let's say about 75 amps... or more than a lot of batteries capacity in one hour. A 36" flat screen will use about 15-20 amps as well. This kind of use is way to much for charging by wind and solar. Suggest you look into small generators.
Finally...before we into an extended help session...read the articles on batteries & systems here on sailnet http://www.sailnet.com/collections/g...ical/index.cfm
...They'll answer most of your questions....we're here for the rest!