To be fair to them, if Blueyonder started offering tech support on home networks as standard we'd probably see our subscriptions rocket to cover the cost.
Anyway, that doesn't help you! From what you've said, my guess is the ethernet port on the modem isn't powered up - possibly faulty. You tried the cable between the router and laptop successfully (you had disabled the wireless first hadn't you?
) but get a disconnected message when trying it between the modem and laptop. (BTW - are we right in assuming that the USB lead was completely unplugged from the modem?)
Try calling Blueyonder back again. This time don't even mention the LAN stuff - just tell them that you need the modem to work over ethernet to the laptop as you need the USB port on the laptop for something else (printer for example). That should remove any complications from the call. Once you can get the modem and laptop talking directly it should be a simple matter to power down modem, router and laptop, re-wire and then power up modem, router and laptop.