Hello,
May I know how are the printer and the cc machine physically connected to the same phone line? Are there any other devices/phone being connected to the same phone line, or connected to the extension port of the printer?
And what is the printer frontpanel displaying? Is the phone/handset icon showing that the phone line is busy?
Are you using a DSL phone line? If yes, you may need to use a DSL filter. This means that your phone cable from the printer should be inserted into the DSL filter, and the filter inserted into the phone jack.
Could you try switching off the printer while leaving it connected to the phone line, does the cc machine still show line is busy? And does the cc machine still able to dial up at this point?