上記のコードをテストしましたが、正常に機能しているようです
static void Main(string[] args)
{
WebClient client = new WebClient();
NameValueCollection values = new NameValueCollection();
values["image"] = Convert.ToBase64String(File.ReadAllBytes(@"C:\test.jpg"));
values["key"] = "the_key";
byte[] responseBytes = client.UploadValues("https://api.imgur.com/2/upload.xml", values);
string response = Encoding.Default.GetString(responseBytes);
client.Dispose();
/* Content of response
<?xml version="1.0" encoding="utf-8"?>
<upload><image><name/><title/><caption/><hash>E63BcFm</hash><deletehash>zWO2xnca2co0VcB</deletehash><datetime>2013-02-15 23:15:45</datetime><type>image/jpeg</type><animated>false</animated><width>677</width><height>342</height><size>29513</size><views>0</views><bandwidth>0</bandwidth></image><links><original>http://i.imgur.com/E63BcFm.jpg</original><imgur_page>http://imgur.com/E63BcFm</imgur_page><delete_page>http://imgur.com/delete/zWO2xnca2co0VcB</delete_page><small_square>http://i.imgur.com/E63BcFms.jpg</small_square><large_thumbnail>http://i.imgur.com/E63BcFml.jpg</large_thumbnail></links></upload>
*/
}