How do I check a WebClient Request for a 404 error

you can try this code to get HTTP status code from WebException or OpenReadCompletedEventArgs.Error:

HttpStatusCode GetHttpStatusCode(System.Exception err)
{
    if (err is WebException)
    {
        WebException we = (WebException)err;
        if (we.Response is HttpWebResponse)
        {
            HttpWebResponse response = (HttpWebResponse)we.Response;
            return response.StatusCode;
        }
    }
    return 0;
}

WebClient will throw a WebException for all 4xx and 5xx responses.

try {
    downloader.DownloadFile(videoAddress, videoPath);
}
catch (WebException ex) {
    // handle it here
}

Put the try catch inside your foreach Loop.

 foreach (string[] i in textList)
 {
    try
    {
        String[] fileInfo = i;
        string videoName = fileInfo[0];
        string videoDesc = fileInfo[1];
        string videoAddress = fileInfo[2];
        string imgAddress = fileInfo[3];
        string source = fileInfo[5];
        string folder = folderBuilder(path, videoName);
        string infoFile = folder + '\\' + removeFileType(retrieveFileName(videoAddress)) + @".txt";
        string videoPath = folder + '\\' + retrieveFileName(videoAddress);
        string imgPath = folder + '\\' + retrieveFileName(imgAddress);
        System.IO.Directory.CreateDirectory(folder);
        buildInfo(videoName, videoDesc, source, infoFile);
        textBox1.Text = textBox1.Text + @"begining download of files for" + videoName;
        if(Download(videoAddress, videoPath) == false)
        {
           //Download failed. Do what you want to do.
        }
        textBox1.Text = textBox1.Text + @"Complete video for" + videoName;
        if(Download(imgAddress, imgPath)== false)
        {
           //Download failed. Do what you want to do.
        }
        textBox1.Text = textBox1.Text + @"Complete img for" + videoName;
    }
    catch(Exception ex)
    {
        //Error like IO Exceptions, Security Errors can be handle here. You can log it if you want.
    }
 }

Private function to Download file

 private bool Download(string url, string destination)
 {
     try
     {
         WebClient downloader = new WebClient();
         downloader.DownloadFile(url, destination);
         return true;
     }
     catch(WebException webEx)
     {
        //Check (HttpWebResponse)webEx.Response).StatusCode
        // Or
        //Check for webEx.Status
     }
     return false;
 }

You can check the WebException for status. Depending upon the error code you can continue or break.

Read More @ MSDN

• WebClient
• WebException.Status
• WebExceptionStatus

Suggestion

• Use Path.Combine to create folder path.
• Can use String.Format to join two strings, instead of +.

Hope this works for you.

If you specifically want to catch error 404:

using (var client = new WebClient())
{
  try
  {
    client.DownloadFile(url, destination);
  }
  catch (WebException wex)
  {
    if (((HttpWebResponse) wex.Response).StatusCode == HttpStatusCode.NotFound)
    {
      // error 404, do what you need to do
    }
  }
}

Or, using C# 7 or later:

using (var client = new WebClient())
{
  try
  {
    client.DownloadFile(url, destination);
  }
  catch (WebException ex) when
        (ex.Response is HttpWebResponse wr && wr.StatusCode == HttpStatusCode.NotFound)
  {      
    // error 404, do what you need to do
  }
}