Getting the internet to work on an old laptop

Hello,
I am trying to re-use my old Toshiba Satellite lap top for my kids.
It was a great little lap top about 5 years ago and I was able to access the internet by plugging in by phone cable and dialing up a number - through free serve I think.
In our house we now currently have a desk top with a wireless router - Netgear that works well on the desk top and my work lap top.
BUT - I cannot work out how to get any access via broad band on my old lap top!
I have tried plugging in directly my Ethernet cable and the netgear start up disk.... but am having no luck at it even recognising that the cable has been attached...
Is this something to do with a modem? Do I need to attach an external modem?

When I can actually get this working I have purchased a wireless USB adaptor so that we can access our wireless service on the lap top - however at the moment I appear to be falling at the 1st hurdle!!!
Any thoughts?