The Background.

At the moment, I have two computers on my small home network, both connected by ethernet cables to a Belkin N1 wireless router.
I have cable broadband with VirginMedia as my ISP and the email software on both computers is Outlook Express 6 (with IE ver. 6).
On one computer, I have my personal email address, provided to me by VirginMedia, as the only mail account in Outlook Express, while on the other I have a different email address, albeit also provided by VirginMedia, as the only mail account in Outlook Express.

The Problem.

This issue occurs when I have both computers running simultaneously:

On the computer that's been turned on first, I can send&receive in Outlook Express without a problem and can access any website I choose.
However, on the computer that's been turned on second, I get an error message saying "The connection to the server has failed...Error no.: 0x8000CCC0E" when I try to send&receive in Outlook Express.

Meanwhile, I can log in to both email accounts fine via webmail on either computer.

Interestingly (perhaps), the one website I can't access on the computer that's been turned on second is www.virginmedia.com.

I've been thrown back and forth between the Belkin and VirginMedia technical helplines in search of an explanation and have reached the end of my tether. Can anyone here please help?!