As another thought, you might be able to right-click on your existing connection (on the old PC) and select Copy, now put a floppy disk in the drive and navigate to it through My Computer, once the drive listing comes up try right-clicking and selecting paste.
You might be able to simply transfer the connection across this way, not sure though.....
Been a long time since I've had dial-up

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Or you could just do as paul says and use the original disk again

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You'll still need your user name and password though.