When I moved to this house 4 years ago the previous owner had Tiscali Broadband - I arranged to have BT Broadand on day one.
It took dozens of calls over 4 weeks and a letter to the Chairman of BT to get connected even though I had given 3 week's notice before moving.
It used to be like this - Tiscali can take up to 10 working days to tell BT that the contract between them has ceased. BT can take up to 5 working days to make the change and switch off Tiscali (all the lines and equipment belong to BT - they just rent it out to other Broadband suppliers). Then perhaps another day or two before BT get around to connecting it to Sky.
You may have fallen into this pit of despair - I hope not.
You have a 24/7 support line to Sky I think - see what they say. You might also try to connect the laptop to the new router using an ethernet cable as a temporary measure and to see if there's any "internet" getting through.
To check the wireless connection -
On the Laptop follow:
Control Panel
Network Connections
then right click on the Wireless Icon and select STATUS and see if there's any signal strength and if "packets" are being sent and received...
Peccavi
December 2008