A while ago I made a small script to manage this, although it wasn't because I ran into the same problem you're having. I just wanted to be able to start and wait for WWW requests from any script, whether or not it's a MonoBehaviour. I ended up writing a script which creates a temporary GameObject for the purposes of using coroutines to monitor the downloads.

So, very roughly speaking, I have a script called "WWWLoader" which is a central script for handling all downloads and http requests. In that script is a static property called 'instance'. This is a property in the c# sense. It uses the singleton pattern to create a single instance of itself, although while it does so, it creates a new temporary gameObject to attach itself to. So the first time 'instance' is used, it gets set up correctly for use, and any subsequent times, it uses the reference that was already made, like this:

private static WWWLoader s_Instance = null;

public static WWWLoader instance
{
    get
    {
        if (s_Instance == null)
        {
            GameObject obj = new GameObject("_WWWLoader");
            s_Instance = (WWWLoader)obj.AddComponent(typeof(WWWLoader));
        }
        return s_Instance;
    }
}

Now, we have an active GameObject, so we can use coroutines on it. So, we can set up a static method which calls on the instance to start a coroutine that waits for the WWW request to complete:

public static void Load(string url)
{
    WWW www = new WWW(url);
    instance.StartCoroutine(WWWLoader.instance.WaitForLoad(www));
}

And then we need to implement the corresponding instance method (which is the actual coroutine function):

public IEnumerator WaitForLoad(WWW www)
{
    yield return www;

    if (www.error != null)
    {
        Debug.Log("WWWLoader Error - \"" + www.url + "\" : "+ www.error);    
    } else {
        Debug.Log("WWW completed!");
    }
}

This now means that - from any kind of script, including non-monobehaviours - you can call this static function (no need to instantiate anything yourself) to start a WWW download:

WWWLoader.Load(url);

This is an extremely simplified version of the script, for illustrative purposes. In practice, you would almost certainly want to add better error handling, an event/callback system to notify the original object which made the request when the download has finished, and possibly even a queue system if you are using it to download a sequence of requests. But I hope it gives you some pointers in the right direction!

Have you checked that the server is actually serving up the file that you're requesting? (eg, by trying the file url in your browser's address bar?).

Some servers (IIS) require that you explicitly set up the correct mime type for all types of files that you want to serve, so if your file has an extension that isn't yet set up with a correct mime type, the server will just act like the file isn't there to clients. This could be the problem.