Wow, that is rusty! I actually have an identical fixture -
link here. With all that rust, the contacts in the starter sockets and lamp holders are probably quite corroded, but they should clean up with some abrasive and elbow grease. Also check that the wires coming out of the ballast aren't shorting to the casing - the insulation often gets quite brittle there. If the ballasts work, heat shrink tubing or liquid electrical tape will help keep the wires insulated near the casing, and new wires can spliced onto them. (I've opened ballasts and replaced wires that way, but that is a lot of work, and you need to be careful around the capacitor inside which often contains PCB oil.)
Overall, that fixture should look nice once you complete the restoration!