Joan1,
I assume your telephone works normally and you can make voice calls. Note that BT can only check the line from the exchange to the master socket in your house. The check does not include any extension (slave) sockets that may be added to your master socket.
Are you plugging your laptop directly into the master socket or do you use an extension socket?
Try unplugging all phones, faxes and doubler sockets (the little plug-in sockets that allow 2 devices to be plugged into 1 socket).
Plug the modem lead directly to the master socket.
Does the modem dial up? If not are there any error messages?
Can you hear the modem handshaking with your ISP's modem (the whistling and screeching noise).
Do you get to the veryifying username and password message?
Are you witholding your telephone numberor ex-directory? Some ISP's won't allow you to connect as they use Calling Line Identity. Add 1470 to the front of the telephone number you dial to your ISP.
Let us know how you get on
Malky