Unable to Access Internet Despite Adapter Showing "Connected".

Question

Hi, I have a Lenovo "G"-Series notebook, Type 4446-38U which has suddenly stopped allowing me to access my internet connections.  The PC is only about a month old.  It is running XP Professional. 
I have three connection options:  1) dial-up (using an onboard HDAudio Soft Data Fax Modem with Smart CP); 2) ethernet or Local Area Connection (using an onboard Broadcom Netlink Fast Ethernet); and 3) wireless (using an onboard Intel WiFi Link 5100 AGN) -- none of these components are showing that they have conflicts/problems in the System Properties/Device Manager. 
At my home, which is located in a rural area where I can only get dial-up, I tried checking my e-mail last week (with Mozilla Thunderbird), but received an error notice stating that the e-mail server could not be found; it was the same issue, when I tried to get Norton virus updates (Internet Security 2009), XP updates on the Microsoft website (using Microsoft Updates with Internet Explorer), and simply accessing the web (using Mozilla Firefox) -- i.e., "Server Not Found."  The odd thing is that I can not only hear the connection being made by the modem, but can also see that the device is 'Connected', when I check the connection in Control Panel/Network Connections.  The following day at my office, I checked the other connection options (ethernet & WiFi), and found that I had the same problem -- i.e., they were shown as "Connected" in Control Panel/Network Connections, but I was unable to access anything on the web (e.g., e-mail, Google, virus/Microsoft updates, etc.).  It's as if there is something blocking the internet connection to these programmes/utilities. 
When I ran the Microsoft Networking Troubleshooter ('Diagnose Network Configuration & Run Automated Networking Tests), all the Network Adapters were shown as having passed.  Ditto, when I ran the "Test a TCP/IP Configuration Using the Ping Command" -- pinging 127.0.0.1, the results showed 4 packets sent and 4 received.
I spent several hours on the phone with Lenovo Tech Support to no avail, and their instruction that I uninstall Norton Internet Security made no difference either.  When they instructed me to open a Command Prompt and ping 192.168.1.1, the results showed that there were 4 packets sent and 4 received.  When I was instructed to ping the IP Address for the wireless adapter, the results showed 4 packets send and 4 received.  When I was instructed to ping www.google.com, the results showed that the ping request could not find the host www.google.com.  Lenovo Tech Support stated that there was nothing further they could do, and that I needed to use a utility to set everything back to factory specs (i.e., have a utility programme erase everything on the hard drive and reinstall XP ... and even then I was told that there was no guarantee that would fix things, meaning that the PC would then have to be sent into their repair depot).  Before I do this, I was hoping that someone here might know as to what's going on with my connection problems and how it could be fixed, without having to erase everything.
I would appreciate any insight or advice anyone might have.  Thanks so much!
~ Jack

Answer 1

I did do a complete uninstall of Norton (i.e., didn't save any of the settings), but that didn't resolve the connection problem.  I also turned off Microsoft's firewall as well, once Norton was uninstalled (it had been turned off, when Norton was installed, and once Norton was uninstalled, MS firewall defaulted back to an on/active status).
I also forgot to mention in my initial description of the problem and actions taken thus far to try and correct it, that I additionally tried the "ping" procedure described in paragraph five above in Windows Safe Mode with Networking, but was still unable to connect to the internet.