There are a number of different reasons why your car is not starting after your Neon overheated while driving.
Since you stated that you brought the car home and parked the car, I am assuming you continued to drive while it was overheating?
If this is the case, it is very likely that you damaged the engine and this is why it won't start.
You may want to have it towed to your auto repair shop. Tell them the sequence of events and then they can determine if there is any life left in the engine.
FYI: If an engine overheats, you want to immediately find a safe place to pull over, turn off the car and have it towed to your garage of choice. This could save your engine and a whole lot of trouble and money!
〉 Answered on Mar 4th, 2014 by Amy Mattinat, Owner and Author at Auto Craftsmen Ltd
The engine might have severe damage from overheating. Start with checking the oil, make sure it is between the marks on the dipstick and does not look like chocolate milk. You can also try pulling out a spark plug (or tow it to a shop and have them do it) and see if there is fluid in the cylinder (it should be dry). If the cylinder is wet or the dipstick looks like chocolate milk, this would indicate a head gasket issue.
If there is engine damage, and you choose to have it repaired, keep in mind that the original cause of the failure may not be able to be determined until the engine is capable of running.
〉 Answered on Mar 4th, 2014 by Helaine Kurot, Owner/Technician at 360 Automotive