The Classic has a ROM Disk you can access with Option-Apple-X-O buttons held down when you turn it on. From here you can put in a floppy disk to format and put in a copy of that system on the disk. while formatting or file copying, if the screen jitters, the analog board needs to be recapped like Uniserver said.

Also you should check for cracked solder joints on the wire harness on the boards (logic and analog). Any cracked solder joint you should desolder, clean the area and resolder with fresh solder and flux. Reflowing the old solder will not last long as a repair. It will fix the cracked joint but it will crack again in a couple of months. Fresh solder makes the repair last a lot longer, by years instead on months.