Reading data from XmlNode response from a SharePoint web service

I am trying to read data from the response from the SharePoint Lists web service. My code is attached and it is pretty much straight from the MSDN library for returning list items using the SharePoint Lists web service. But when I loop through the XmlNode (nodeListItems) that presumably contains the data, on the second loop through, I get an XML stream in the innerXml string that appears to have everything that I need. What I cannot figure out from MSDN is how to properly read this data. There are 3 listItems in every one of these responses and only the second listItem has any useful data. Do I create an XmlNodeReader only on the second listItem? Am I on the right track?

I have read numerous online postings on reading XmlNodes, but I have not puzzled this one out.

string siteUrl = Properties.Settings.Default.SharePointSiteUrl;
                string libraryGUID = Properties.Settings.Default.LibraryGUID;

                SPListService.Lists spLists = new SPListService.Lists();
                spLists.Url = siteUrl + @"/_vti_bin/lists.asmx";

                spLists.Credentials = System.Net.CredentialCache.DefaultCredentials;

                // Instantiate an XmlDocument object
                System.Xml.XmlDocument xmlDoc = new System.Xml.XmlDocument();

                string listName = libraryGUID;
                string viewName = "";
                string rowLimit = "500";

                /*Use the CreateElement method of the document object to create elements for the parameters that use XML.*/
                System.Xml.XmlNode query = xmlDoc.CreateElement("Query");

                System.Xml.XmlNode viewFields =
                    xmlDoc.CreateElement("ViewFields");

                System.Xml.XmlNode queryOptions =
                    xmlDoc.CreateElement("QueryOptions");

                query.InnerXml = "<Where><And><Eq><FieldRef Name=\"CONTRACT_NO\"/><Value Type=\"Text\">" + contractNo + "</Value></Eq>" +
                    "<Eq><FieldRef Name=\"ACTIVITYTYPE\"/><Value Type=\"int\">" + activityType + "</Value></Eq></And></Where>";

                viewFields.InnerXml = "<FieldRef Name=\"CONTRACT_NO\" />" +
                    "<FieldRef Name=\"ACTIVITY\" />" +
                    "<FieldRef Name=\"ACTIVITYDATE\" />" +
                    "<FieldRef Name=\"DOCCATEGORY\" />" +
                    "<FieldRef Name=\"DOCSTATUS\" />" +
                    "<FieldRef Name=\"DOC_TYPE\" />" +
                    "<FieldRef Name=\"RECEIVED\" />" +
                    "<FieldRef Name=\"FIRSTVIEWDATE\" />" +
                    "<FieldRef Name=\"REFNO\" />"; 

                queryOptions.InnerXml = "";

                System.Xml.XmlNode nodeListItems = spLists.GetListItems
                    (listName, viewName, query, viewFields, rowLimit, queryOptions, null);

                foreach (System.Xml.XmlNode listItem in nodeListItems)
                {
                    string innerXml = listItem.InnerXml;
                    docCount++;
                }

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