AudioClip not playing

I have an audio clip that I'm trying to have start when a certain condition is met. The clip is being attached through the script I'm running which is supposed to be played using the AudioSource component attached to the GameObject. The clip is not playing, however. The variable holding the clip is a public AudioClip and it is being set within the inspector. Setting the AudioSource to play on awake would work at this point, but would not at a later time, so I want to avoid doing that. Does anyone have any suggestions?

C#

     using UnityEngine;
 using System.Collections;
 
 public class MoveCar:MonoBehaviour{
     //Car's idle speed
     private int idleSpeed = 0;
     //Car's current speed
     private float speed = 0.0f;
     //Car's top speed
     public float topSpeed = 165.0f;
     //Car's acceleration rate
     public float acceleration;
     //Car's braking power
     public float deceleration = 15f;
     private Rigidbody playerCar;
     private AudioSource engine;
     public AudioClip carStartAudio;
     private bool starting;
 
     void Start(){
         playerCar = GetComponent<Rigidbody>();
         engine = playerCar.GetComponent<AudioSource>();
         starting = true;
         if(starting){
             engine.clip = carStartAudio;
             if(!engine.isPlaying){
                 engine.Play();
             }
             Debug.Log(engine.clip);
         }
     }
 
     void Update(){
         if(Input.GetKey(KeyCode.W)){
             float horizontal = Input.GetAxis("Horizontal");
             float vertical = Input.GetAxis("Vertical");
             if(speed <= topSpeed){
                 speed = speed + (acceleration * Time.deltaTime);
                 Vector3 movement = new Vector3(vertical, 0f, horizontal);
                 playerCar.AddForce(movement * Mathf.Clamp(speed, idleSpeed, topSpeed));
                 Debug.Log(speed);
             }
             else{
                 speed = topSpeed;
                 if(speed == topSpeed){
                 }
             }
         }
     }
 }

If anyone would like to actually see what's going on, I've uploaded the game to my Dropbox, feel free to take a look.