are you sure the n300 is modem router and not just a router?
if you can use quick setup and enter username
password if required cab be anything but often just BT will do
reset netgear and start again
I would also initially use an ethernet cable from laptop to router until set up
Try setting it up before you connect to the telephone socket. Just connect the Ethernet cable to the router and your laptop and enter the routers set up pages and enter the BT log on details. Once you have entered and saved the details then plug it into the phone socket.
Are you on ADSL or Fibre broadband?
The only reference I can find for a N300 modem router is the DGN2200 which is ADSL only.