Well, try to uninstall completely the network driver and the software by using application like Uninstaller 2008/09.
Then re-install the drivers:
Is the LAN enabled in the BIOS?
Does the LED on the network card light up?
Try to ping the ip address 127.0.0.1?
If the external ethernet adapter also does not work, this means the problem is somewhere else, because the external card has nothing to do with the onboard network card. It is unlikely to have both the onboard network port failed and the pci slot as well.
So, i will suggest you to try to start from beginning again.
Update the bios to the latest version.
Make sure that the onboard components are enabled in the bios.
Install another OS like Windows Vista/7. Dont use the same OS like before, or you can use
another version of Windows XP CD.
Install the latest drivers from the website.
Inf, gfx, audio, lan, etc.
Check if it works at least.
Note: if you are using Windows 7 as a test, you will need to extract the LAN driver to make it work.
Thanks, friend. I have done all of what you have suggested. The PCI ethernet card's LED blinks and the modem's link LED also lights up (doesn't do with the onboard LAN) but I am not getting the Local Area Connection in the Control Panel and so am not able to configure it. The onboard LAN is enabled in the BIOS. It started going off periodically for a couple of weeks and then stopped altogether two weeks back. I'll try all the things again just to see what could be wrong and if it could be set right. I have already ordered a quad-core processor and a DG43NB board. Hope things work out okay in the new setup.