I was big into stereos (and am still into many things AV) when turntables ruled the proverbial roost for audio equipment. What you have is a belt drive turntable. Belts wear out and break or just break because the rubber rotted out.
To restore this baby, the first question, since you have it opened up, does the drive motor still spin? If it does, then you all you need to do is just get a belt. That I cannot help you with, as I have been out of turntables for some time. If you cannot find one (I bet you can on the net), then look around where vacuum clear repair parts are sold. The length needed for a rubber belt will be about a quarter inch length than the physical distance between the motor and the turntable's outer pulley length. Just enough short to create tension on the rubber pulley.
The next challenge and probably not a real big one, is determining whether or not the cartridge stylus is any good. If it is still good (they are very fragile), then you are good to go after the new belt goes on.
Styluses are pricey these days as they are not mass produced anymore. Can you post a pic of it? That can be the deal killer for an economical restoration. The price of a replacement belt is pretty trivial compared to styluses.
