Ethernet connection not working?

Before I start I would like to point out that I am not particularly great with computers so any help I am given will be great!

I have recently purchased an Inspiron 6000.

I have been trying to go wireless. I am able to connect to the internet wirelessly as I can use my neighbour’s wireless router.

I have purchased my own wireless router (Netgear 54 Mbps (WGR614)).

However the problem I have is that when I connect my computer to my Telewest Broadband modem via the Ethernet port on the back of my machine no connection is available. The light on the modem indicating PC connectivity does not light up.

When I try the Ethernet connection from the modem to the router the light on the modem flashes furiously to indicate PC connectivity.

From this I have determined that the Ethernet connection on the back of my Inspiron is not working.

Does it need to be activated in some way?

Is there any more scientific way that I can check this out?

And is there any way that I can correct this without sending the computer back to Dell?

Thank you for any assistance as I have wasted hours on evenings this week!!!

Craig