[DllImport("wininet.dll")]
        private extern static bool InternetGetConnectedState(out int connectionDescription, int reservedValue);

        public bool IsInternetConnected()
        {
            int i = 0;

            return InternetGetConnectedState(out i, 0);
        }

------解决方案--------------------
AutoResetEvent waiter = new AutoResetEvent(false);
           Ping myPing = new Ping();
           myPing.PingCompleted += new PingCompletedEventHandler(myPing_PingCompleted);
           string data = "OK";  
           byte[] buffer = Encoding.ASCII.GetBytes(data);
           int timeout = 10000;
           PingOptions options = new PingOptions(64, true);
           myPing.SendAsync(_AppState.ServerName, timeout, buffer, options, waiter);  
或
IPGlobalProperties properties = IPGlobalProperties.GetIPGlobalProperties();
           TcpConnectionInformation[] connections = properties.GetActiveTcpConnections();
           foreach (TcpConnectionInformation info in connections) {
               if (info.RemoteEndPoint.Equals(targetEndPoint)) {
                   _AppState.OnlineStatus = Constant.ONLINE_STATUS_ONLINE;
                   isOnline = true;
                   break;
               }
           }
或
   [DllImport("wininet.dll")]
   private extern static bool InternetGetConnectedState(out int connectionDescription, int reservedValue);


  System.Net.IPAddress[] addressList = Dns.GetHostByName(Dns.GetHostName()).AddressList; 
           for (int i = 0; i < addressList.Length; i ++)  
           {  
               s += addressList[i].ToString();  
           }  


------解决方案--------------------
 string st = "";
               ManagementClass mc = new ManagementClass("Win32_NetworkAdapterConfiguration");
               ManagementObjectCollection moc = mc.GetInstances();
               foreach (ManagementObject mo in moc)
               {
                   if ((bool)mo["IPEnabled"] == true)
                   {
                       System.Array ar;
                       ar = (System.Array)(mo.Properties["IpAddress"].Value);
                       st = ar.GetValue(0).ToString();
                       break;
                   }
               }
               moc = null;
               mc = null;


------解决方案--------------------
照顾楼主不认识VB.NET的语法,转换为C#  
C# code

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Windows.Forms;
using System.Net;

namespace WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            WebClient wb = new WebClient();
            String strIP = "";
            String strContent = "";
            Regex regIP = new Regex("\\d{1,3}.\\d{1,3}.\\d{1,3}.\\d{1,3}");
            try
            {
                strContent = wb.DownloadString("http://www.ip138.com/ips8.asp");
                if (strContent.IndexOf("IP地址查询") >= 1)
                {
                    textBox1.Text = "爽,可以上网!";
                    strIP = regIP.Match(strContent).ToString();
                    if (strIP.Trim() != "")
                    {
                        textBox2.Text = "俺的IP是:" + strIP;
                    }
                    else
                    {
                        textBox2.Text = "虽然俺上网了,但是俺是黑户,没IP!";
                    }
                }
            }
            catch
            {
                textBox1.Text = "真不爽,不能上网,我去炸了电信!";
                textBox2.Text = "不能上网,没IP!";
            }
        }
    }
}