Please help! Modem dial-up connection problem

Can someone help me?
I have a HP G60 laptop running on Windows 7 Home Basic. The problem is that I can’t access the internet, using the dial-up connection. I keep on getting error messages. For instance, “There is no dial tone."
When I click on the internet icon, I get a message that, “Connection does not exist, you cannot connect to the internet because you are working offline”. I went to the modem options and unchecked the, "wait for dial tone before dialing" check box and redial the second time. This time round, it started its dialing sound but never connected successfully.
It was taking forever to connect and then a message pops up, "the remote computer did not respond." Strangely, this message pops up whenever the telephone is connected or not connected to the computer.
I checked the modem, its working properly. I went through network diagnostics, troubleshooting and followed all the required instructions but no problem was detected. I have done a reset and setting up a new connection and that has not worked either. I can’t think of any other way to fix this.
I have tried all I can in vain. What I need is help. Has someone experienced the same problem?
Any suggestions?
