There was a recall to replace the vacuum hose for the brake booster. In the presence of oil, the original hose could swell and become disconnected. The brakes would function but power assist would be lost and the pedal would feel very hard.
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Repairpal verified 2001 Dodge Neon problems
A click heard when turning the steering wheel may be solved by aligning the steering column or installing revised parts in the column (requires removal of the steering column).
If a Check Engine Light illuminates indicating leak detection pump (LDP) failure, the cause is often pinched or disconnected vacuum lines to the pump. Vacuum lines should be inspected before replacing the leak detection pump. Contamination (carbon or debris) in the pump can cause failure and any hoses should be cleared before a new pump is installed.
A clicking or popping sound from the front of the vehicle (left or right side) while accelerating from a stop may be fixed by installing a rubber gasket on the axle shaft.