One problem related to underhood wiring has been reported for the 1998 Dodge Neon. The most recently reported issues are listed below.
My daughter was driving the car, when it became stuck in the snow. She was not rocking the car, only sitting in it waiting for someone to come with a shovel, and noticed flames shooting out from under the hood. She got out of the car, and went and called for help. The car was totally consumed in flames in a matter of minutes, and was a total loss. I feel there was a problem with the engine. I have found a couple of sites on the web that mention recalls due to engine overheating, but we were never contacted to bring the car in for service.