This is getting off to a really bad start. I think I'd void the purchase if you have that option, because something is definitely not on the up and up here. If it was marked "used", then it was previously registered; if it were a demo, it would still be on the manufacturer's certificate. This is called an MSO (Manufacturer's Statement of Origin) and is used by DMV to first title the vehicle.
Added to the murky status of the car is the breakdown, which is not a good sign.
So unless you got the deal of a lifetime on this car, I"m personally not keen on your keeping it. Other folks might have a different opinion--it's just how I would react.