@CalamityJane,
There are people that buy repairables. They often advertise "best price for junkers." If the body is in good shape and the car is reasonably new then you might be able to find someone willing to put a new engine in it.
A few things.
1. You need a clean title on the car - preferably no accidents and the car can't have been totaled for sure. Some states mark the title "salvage" when a car is totaled.
2. The car needs to have a blue book value when running to make it worth while for someone to fix it. An engine and labor can cost about $5,000. No one is going to pay $250 for a car that is only worth $2000 when running.