Collision and character controllers

I have a simple character with collision and a rigidbody and some static boxes without rigidbodies which makes up the level. The character however falls through the boxes. Now this might seem simple enough, I Just need to add a character controller right. The problem is that I want my character to be capable of flying and I don't really care about jumping or sliding on slopes. Is there any way for me to create terran collision like this? I assume I'd have to program physics by myself and that's maybe not such a good idea considering I'm not really a good programmer. So, what can I do to remedy this...?

Here's my movement script if anyone is interested

 using UnityEngine;
 using System.Collections;
 
 /// <summary>
 /// Movement.
 /// 
 /// This script controls the player movement.
 /// </summary>
 
 public class Movement : MonoBehaviour {
     
     public int acceleration = 20;
     private Vector3 velocityToBeApplied;
     private Transform playerTransform;
     private int stopSpeed = 3;
 
     // Use this for initialization
     void Start ()
     {
         if(networkView.isMine == true)
         {
             velocityToBeApplied = Vector3.zero;
             playerTransform = transform;
         }
         else
         {
             enabled = false;
         }
     }
     
     // Update is called once per frame
     void Update ()
     {
         if(Input.GetButton("MoveLeft"))
         {
             velocityToBeApplied = new Vector3((velocityToBeApplied.x - acceleration) * Time.deltaTime,
                                                 velocityToBeApplied.y, velocityToBeApplied.z);
         }
         
         if(Input.GetButton("MoveRight"))
         {
             velocityToBeApplied = new Vector3((velocityToBeApplied.x + acceleration) * Time.deltaTime,
                                                 velocityToBeApplied.y, velocityToBeApplied.z);
         }
         
         if(Input.GetButton("MoveForward"))
         {
             velocityToBeApplied = new Vector3(velocityToBeApplied.x, velocityToBeApplied.y,
                                                 (velocityToBeApplied.z + acceleration) * Time.deltaTime);
         }
         
         if(Input.GetButton("MoveBackwards"))
         {
             velocityToBeApplied = new Vector3(velocityToBeApplied.x, velocityToBeApplied.y,
                                                 (velocityToBeApplied.z - acceleration) * Time.deltaTime);
         }
         
         if(Input.GetButton("MoveUp"))
         {
             velocityToBeApplied = new Vector3(velocityToBeApplied.x, (velocityToBeApplied.z + acceleration) * Time.deltaTime,
                                                 velocityToBeApplied.z);
         }
         
         if(Input.GetButton("MoveDown"))
         {
             velocityToBeApplied = new Vector3(velocityToBeApplied.x, (velocityToBeApplied.z - acceleration) * Time.deltaTime,
                                                 velocityToBeApplied.z);
         }
         
         playerTransform.Translate(velocityToBeApplied);
         
         velocityToBeApplied = Vector3.Lerp(velocityToBeApplied, Vector3.zero, Time.deltaTime * stopSpeed);
     }
 }