Problems connecting to xbox live?

We have a wireless router for our broadband internet connection that links to the xbox for xbox live service and also to the laptop. Whenever the laptop is turned on the internet will work fine, but if i turn it off and connect to the xbox, it refuses to work even after re-booting everything, switching off the modem etc. if the laptop hasnt been on at all, the xbox connection will work fine. my laptop is an aspire 3680... does anyone have any ideas on why it's doing this? any help would be appreciated, thank you