Can I park at Ballymoney railway station and continue my journey by train?

Yes.

Ballymoney train station is an official rail Park and Ride location. Drive to the station parking area and then use the Belfast–Coleraine–Derry rail network for destinations served by the trains stopping there. Do not mistake the town’s other council parking areas for the railway Park and Ride: those may have different restrictions and longer walks to the platform. Check the station’s accessibility and the train schedule if you are leaving early or returning late.