Can I make a Faraday cage for a car's motor?

You can, but you are then speaking about mothballing a car because all of the sensitive electronic components need protected. You may wish to look at a bicycle motor if you are mechanically inclined, or perhaps an old, old car or surplus jeep: no electronics. A Model T replica, or an actual, maybe a Willy's or something. Heck a golf cart with a lawn mower engine might be what you like best, or you might just be better off with a horse or a good mule because they can thread their way through the throngs of cars that were turned into boulders. Best wishes either way!