External Answering Machine Hook up with M7310

Yes. Hook the external answering machine up, and turn the built-in one off.

You have unheard messages on the voicemail system provided by your telephone company. This system records messages when someone calls while you're already on the phone.

Please contact your telephone company for instructions on accessing their voicemail system.

The CS6419 isn't an answering machine. To gain access to your voicemail, please consult the documentation for whatever answering machine or voicemail system you have on your telephone line.

If you require further assistance, please add a comment to this question identifying the answering machine or voicemail system.

Are you referring to the messages on your answering machine? If so, what model Uniden phone/answering machine?

Or are you asking about the voicemail system provided by your telephone company? If so, contact your telephone company for instructions on accessing their voicemail system.

What model Uniden DECT 6.0 phone/answering machine?

Are you sure the message in on your answering machine and not a voicemail system provided by your telephone company? Many telephone companies offer a voicemail system that takes messages if someone calls while you're already on the phone.

The ring count is controlled by the answering machine or voicemail system on your phone line. The TRU9260 is just a phone, it will ring until your or the answering machine/voicemail system picks up.

What answering machine/voicemail system do you have?

The GZ5838 isn't an answering machine. If you have a separate answering machine connected to your phone line, please refer to its documentation. If you subscribe to a voicemail system offered by your phone company, please contact them for information and help.
The GZ5838doesn't have speakerphone capabilities.
You may download a copy of the manual here.

Sounds like the answering machine is picking up the telephone line and not releasing it.

Hence the busy signal, cause the answering machine has the line off hook. It's like leaving your telephone off hook, the next caller will get a busy signal...

The answering machine might be bad... have you noticed that you were talking on the phone and hung up then the next call would be the busy signal? Maybe test this out.
Do you have the correct voltage to the answering machine, too much power or too little power can do funny things to telephone equipement.

Issue: How do I connect a telephone, answering machine or computer modem to my machine?
Solution: Connecting the telephone line and external devices to the MX310

Preparing the Machine for Faxing Typical examples of connecting the machine are described below. The machine cannot send/receive faxes if the connection is incorrect. Connect the machine correctly.

Important

If the Power Disconnects Unexpectedly

If there is a power failure or if you accidentally disconnect the power cord, the date/time settings as well as all documents stored in memory will be lost. User data and speed dialing settings are retained. If the power disconnects, the following will apply:

You will not be able to send or receive faxes or make copies.

If a telephone is connected to the machine, you can receive voice calls.

Whether you are able to make voice calls depends on the type of your telephone.

Methods of Connecting External Devices Connecting to an Analog Line
(A) Telephone line (analog)

Connecting a Telephone or Answering Machine Directly
(A) Telephone or Answering machine

Important

Do not connect the machine and external devices in parallel to the same telephone line using a splitter (A) . The machine may not operate properly.


Connecting a Telephone or Answering Machine via a Computer
(A) Computer

(B) Telephone or Answering machine


Methods of Connecting the Various Lines The following are some basic connection schemes that apply when you are connecting to a non-analog telephone line. These are examples and are not guaranteed to suit every connecting conditions. For details, refer to the instruction manual supplied with the network device (control devices such as an xDSL modem, terminal adapter, or dial-up router) you are connecting to this machine.

Connecting to an xDSL
(A) Digital Subscriber Line

(B) Splitter

(C) xDSL modem (splitter may be built-in to the modem)

(D) Computer

Connecting to an ISDN Line For details on ISDN connection and settings, see the manuals supplied with your terminal adapter or dial-up router.

Please be informed that you can access Canon's online support site for your printer by clicking here. You can find many solutions to your problems by searching their database once you have navigated to the support page for your model.
I hope this information allows you to resolve this issue. If not, reply back with a comment to this thread.
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change how many rings your voicemail picks up in or cancel it.
set your answering machine to less rings than your voicemail.