Hi
Id go and get yourself an ethernet car for a start off, about £9.99 from PC world or £3 - 4 online. It also sounds to me like you have brought the right router. The Linksys WAG354G does have a modem built in and I would expect it behave in the same way as the one you brought but in contrast to the above poster I disagree that it can not be used for cable connections, as the WAG354G can and it is from the same family. As I use the WAG354G.
What I suggest you do is if you need a modem to connect and I expect your blueyonder box is a modem then ditch it but make sure you know you user name and password. Then connect from the wall into the modem and enter the set up menu
http://192.168.1.1 (I think thats right), enter all your info and save settings and hopefully you should be getting somewhere.
A good start would be making 100% sure if you are on ADSL or Cable?