So you have proved that there is nothing wrong with the telephone line as the AOL software and modem gives you a connection. That seems to me to leave only one thing, the router itself. I believe that AOL demands that Maximum Transmission Units (MTU) must be set at 1400 not 1492 which is the default. Have you gone into the router setup and done that?
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Do you know that we're all in line for succession to the throne? Really?
Well, if forty-eight million, two hundred thousand, seven hundred and one people died I'd be Queen.