I'm certainly not an electrical engineer, but here's what I think is correct.
Solar panels are used to recharge batteries. Then you run everything off the batteries. You can also use wind power to charge the batteries.
Using LED bulbs are stuff are pretty helpful here. Big appliances like fridges, washers, dryer, will not run very long on battery power.
You do not need a working utility connection. Hook them up the same way you would a back up generator.
Solar can also be used to heat water. Nobody likes a cold shower.