I think i know what the problem is.
From what i gather you are connecting the laptop directly to the modem, then when you want to play Xbox Live you are disconnecting the laptop from the modem and then connecting the 360, correct?
If you are doing so you need to switch the modem off for 30 seconds before switching between the laptop or xbox 360, when the modem is off connect it to the Xbox 360.
Then switch the modem on again and let it load up and connect, after it has done this power the Xbox 360 on and you should be able to connect to live.
You will then need to do the same when you wish to use the internet on your laptop again.