The automatic transmission in your 1998 Dodge Neon (All other manufactures use very similar systems) uses a torque converter to connect the engine and the transmission. The torque converter is a fluid coupling which allows the engine to idle while the car is stopped in gear, it "slips" to allow this to happen. As the car is driven the torque converter continues to send the engine power to the transmission however there is always some slippage. This slippage became an issue as fuel mileage has become more and more important. These newer torque converters have an electrically operated clutch which will "lock" the torque converter at freeway speeds to eliminate any slippage, thus increasing fuel mileage. The engine control computer controls an electrical solenoid which engages and disengages the torque converter clutch. Most repair shops should be able to read and diagnose any computer fault codes related to the torque converter clutch electrical circuit. There is no way to give a cost estimate until the problem is diagnosed.