Battery help

Putting in my 2 cents. I have been a hobbyist solar for 4 years now. Here goes got to HF/Lowes/Home depot. Tell them you want a device that plugs into the fridge or any other appliance to you can tell how many amps you are drawing off that device. Check them all and write it down. Here is an example how I did mine
Plugged it in the fridge it read 8 amps
Plugged it in the Evap cooler it read 4.5 amps
Plugged it in the TV it read 1.5 amps
Plugged it in the Dvd Player 2 amps amps
Add them all up
I would need Roughly 16 amp Hrs plus what ever the inverter sucks up.

In my home I need 40 Amps an hour. My System has 18 158 watt panels and 12 40 watt panels. .

As Far as a off the cuff two 6 volt 108 amp golf cart Batteries wire to 12 volt would get you 108 divide by 6.5 + 2 amps for the lights (rough estimate check the package)
should get you 12 hrs or very close.
Hint Go to 12 volt 500 lumin LEDs and you can get the lights down to 0.4 amps. You will have to run some wire but the payoff will be real good. The fridge if its older will and the price of the inverter to run it will eat your solar lunch. I have seen the new refrigerators one doing real low amps. The good thing is they are not on all the time

Just a Note as much as you can do 12 volt do it it will pay off in the end. 12 volt TVs LED Lights DVD players are everwhere. You Can Pull this off. Too Bad the wife will get the cash savings ( True in my Case)But planning and Amps

Try using this...

www.batterystuff.com/kb/tools/solar-calculator.html

For the refrigerator, the 6.5 amps is when it is running, remember it cycles on and off.  The 53 kWh.mo is the number you need.
A desktop computer could be between 200 and 500 watts including the monitor.