First get replacement fusible links. I would suggest having backup links as well.
You need Nissan part numbers 24161-A0100 and 24161-28500. You should be able to give those numbers to the parts department at Gwinnett Place Nissan or Stone Mountain Nissan. If neither dealership will help you, you could order them from http://www.courtesyparts.com. In a pinch, you can get the black and green links from http://www.zcarparts.com or http://www.zcardepot.com, but you will pay more.
After you get the replacement fusible links, don't install them. Find the addresses for the best BBQ and best Mexican food places near you. Invite me over to assess what's going on with your electrical system and take me to lunch afterward. Oh, and have a 6 pack of Diet Dew bottles on hand. Don't get the regular stuff. I only drink diet.
I can pencil you in for the weekend of the 19th. That should give you enough time to get the fusible links and have a fully charged battery. I'll show up with the proper diagnostic equipment, and I will probably be able to get your car running or give you a pretty good idea of why it won't run. By the way, I like to get off to an early start so I can be done before the heat of the day.
Also, go to the downloads section here and download the factory service manual: http://www.classiczcars.com/files/category/12-260z/
You should also download a wiring diagram. Here is where you can find one: http://atlanticz.ca/zclub/techtips/electrical.htm. Download the GIF file of the 260Z wiring diagram.
If you want to take me up on my offer, send me a PM with your first and last name, address and phone number.