Your car may be worth $1000 to an uneducated customer… but that’s about it. A 2003 Neon in “good” condition, with a clean title is worth about $1800-2500. To me, a 2003 Neon with a bum motor and a salvage title wouldn’t be worth the gas money to go look at it, even if it was 3 blocks away.
My best advice is to be completely honest about the car’s history and mechanical problems and if a buyer still wants to hand you money for it… that’s their problem.