Hp all in one 5610 wont receive fax and phone line does not go on double ring . incoming fax shows phone off hook when trying to receive fax.no ready appears

Ensure that telephone line connector inserted in line in port(other than telephone symbol port)
In fax settings..
select automatic in answer mode
select ring to answer as 5 rings
select ring mode as all rings(single,double & triple rings)
try for incoming fax.

Check video for 'fax receive set up' in similar model:


Manual receive: In coming call receives like telephone
Fax/tele: Incoming call rings like telephone if its not fax, if incoming is fax it will entered in fax mode automatically
Automatic: Incoming call converts in fax mode after ring count ends( ring to answer option also avail in fax set up mode rage 1-6 rings)
Fax: Incoming calls straight away converts in to fax mode.( this option only for dedicated fax lines)
Set up your best option as per your requirement.

The steps are simple

Connect the 2 wire phone cord at back of printer in EXT 1 ( this is for incoming and outgoing for Fax )

Press the setup button printer
Scroll to Fax Settings
Set the Rings to Answer ( +2 from your Voice mail rings, if someone reaches your voice mail on 4 rings, set 6 Rings to Answer )
On the printer front panel is a Button Auto Answer - turn it ON

You are ready to send/recieve Faxes

For more details about Fax features you can download the manual of this printer from this link
http://h10032.www1.hp.com/ctg/Manual/c00461378.pdf

The answer mode determines whether the HP Fax answers incoming calls or not.

Different answer modes are :

* Fax

The HP Fax will automatically answer all incoming calls using the Rings to Answer setting. This is the default setting.

* FaxTel (unit with handset model only)

The HP Fax automatically answers all incoming calls using the Rings to Answer setting. If the call is a fax call, the HP Fax will receive the fax. If the call is a voice call, the HP Fax will create a special ring to indicate it is a voice call. The incoming voice call will need to be answered using the attached handset.

NOTE: If the HP Fax determines the call is a voice call, only the HP Fax will ring with the special ring tone. The other phones on the same phone line will not ring at all. You will not be able to pick up the voice call using the other phones.

* Tel

The HP Fax will not automatically answer calls. Faxes will need to be received manually.

* AnswerMachine

The HP Fax will monitor the line when an incoming call is answered by a person or by the answering machine. If the HP Fax detects fax tones on the line, it will receive the fax.

It's either your phone, or it's your fax machine that does not support fax through phone.

Receive a fax
Depending on the Auto Answer setting, your HP All-in-One can receive faxes
automatically or manually. If you have set the Auto Answer option to Off, you will
need to receive faxes manually. If the Auto Answer option is set to On (the default
setting), your HP All-in-One will automatically answer incoming calls and receive faxes
after the number of rings specified by the Rings to Answer setting. (The default
Rings to Answer setting is five rings.)
Receive a fax manually
If you set up your HP All-in-One to receive faxes manually (the Auto Answer option is
set to Off) or you answer the phone and hear fax tones,
1. Make sure the HP All-in-One is turned on and you have paper loaded in the input
tray.
2. Remove any originals from the document feeder tray.
3. If you are currently on the phone with the sender, instruct the sender to press
Start on their fax machine.
4. When you hear fax tones from a sending fax machine, do the following:
a. Press Fax on the control panel of your HP All-in-One.
b. When prompted, press 2 to select Receive fax.
c. After the HP All-in-One begins to receive the fax, you can hang up the phone.

Not sure this will help but you could give this setup guide a try and see:

Setting up fax to use DSL

Post back your results, particularly if you need more assistance. Good luck.

Do you have a distinctive ring pattern in the same phone line
If no then you need to get a distinctive rig pattern from your service provider, which will differenciate the type of rings for phone and fax.
If you have a distinctive ring pattern make sure which one it has single rings, double rings, triple rings and double and triple rings.
To enable> First make sure auto answer in turned On
In setup/Menu go to > Rings to answer and set it to 5 or 6, and make sure the rings to answer in you answering machine set to 4(Always Should be lower then you rings to answer in the fax)
In Advance Fax setup> Then Ring pattern should be setup for the one which you service provider as given either double or triple Rings>
And the go to tools and run fax test and check what has failed

Fax machines are designed to have their own dedicated fax line.

Anything else is a **** shoot.

• The Rings to Answer feature might not be set to answer after the
appropriate number of rings for your office setup.
• If you have a voice mail service at the same phone number you use
for fax calls, you must receive faxes manually, not automatically. For
information on how to receive faxes manually, see receive a fax
manually from a phone on page 48.
• If you have a PC modem on the same phone line with your
HP Officejet, check to make sure that the modem’s software is not
set to receive faxes automatically. Modems with this auto fax
receive feature turned on will take over the phone line to receive all
incoming faxes, which will prevent the HP Officejet from receiving
fax calls.
• If you have an answering machine on the same phone line with
your HP Officejet, you might have one of the following problems:
– Your outgoing message might be too long or too loud to allow
the HP Officejet to detect fax tones, and the calling fax machine
might disconnect.
– Your answering machine might not have enough quiet time after
your outgoing message to allow the HP Officejet to detect fax
tones. This problem is more common with digital answering
machines.
The following actions might help solve these problems:
a. Disconnect the answering machine and then try receiving a fax.
If faxing is successful without it, the answering machine might
be causing the problem.
b. Reconnect the answering machine and re-record your outgoing
message. Make sure the message is as short as possible (no
more than 10 seconds long), and that you speak softly and
slowly when recording it. Try again to receive a fax.
• If you have a special ring pattern for your fax phone number (using
a distinctive ring service through your telephone company), make
sure that the Answer Ring Pattern feature on your HP Officejet is set
to match. For example, if the phone company has assigned your
fax number a double ring pattern, make sure Double Rings is
selected as the Answer Ring Pattern setting. For information on
changing this setting, see change the answer ring pattern
(distinctive ringing) on page 63.
Note that some ring patterns cannot be recognized by the
HP Officejet, such as those with alternating short and long ringing
patterns. If you are having problems with a ring pattern of this type,
ask your phone company to assign a non-alternating ring pattern.

http://h10032.www1.hp.com/ctg/Manual/c00095626.pdf