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.Google+
Car Problem Reports
Dodge Neon Clicking or Popping From Front of Vehicle While Accelerating
Dodge Neon Problem
Drive Train Affected: Automatic Transmission
Average Mileage: 71,800 mi (53,000 mi - 92,000 mi)
Vehicle makes popping, straining, squeaking sound... seems like it's coming from dashboard/front of car.
Visitor, 2005 Dodge Neon, 70,000 mi
Same problem area. Clunk/pop noises when starting forward or braking.
Visitor, 2003 Dodge Neon, 90,000 mi
when I excelerate at times not every time but some times I get a quick pop sound just 1 pop then it stops !
I get a slight clunk noice when starting forward and upon braking. Someimes I can feel it through the brake pedal. Not a major noise but worrisome. Car runs fine otherwise.