Hi

You should be able to use the Sky modem but I'd like to suggest something if you would not mind...
First, get a better wireless adapter. The laptop according to ZDnet uses 802.11b which has been now superseded by 802.11g. With prices of USB adapters ever falling you can get a decent one for about £20.

That is not all.... In order to use the Netgear modem/wireless router you will need to mimic the connection settings from the BT modem so when you fire your Netgear up it will connect to your ISP. Have you ever logged in to your BT modem?
This is normally done by typing 192.168.0.1 into the Internet explorer address field. Then you might have to use a username and password to log in to the modem.

Here is the webpage of the hardware I think you have (I am a SKY customer and that is the one I have) Support Page

Check the installation guide and the refrence manuall and see if that gives you an idea...

Let us know how you get on with getting the connection settings from the BT modem