DNS Server not responding help

Hi I am new to the forum and hope its OK to post here. I apologise if I have posted on the wrong topic!! MY internet was working fine up until yesterday and then suddenly it loads a page and the pager times out. I have rebooted the router, I the ran a troubleshooter and it said the DNS Server is not responding (I am on BT Broadband in the UK). I ran diagnostics on my router and it says: -


Test Internet surfing
Test xDSL Synchronization Pass
ATM OAM Segment Ping Pass
ATM OAM end to end Ping Pass
Test PPP Server connection Pass
Test authentication with ISP Pass
Test the assigned IP address Pass
Ping default gateway Fail
Ping primary Domain Name Server Fail
Test DNS Root Fail
Network Connection Status Inspect(NCSI) Fail
Diagnostics completes


I am at a loss as to what to do now and just wondered if some kind person might have some ideas. I would appreciate any help. Kind regards Gail