Unit is able to send FAX, but not Receive a FAX.

You can receive faxes automatically or manually. If you turn off the Auto Answer option, you must receive faxes manually. If you turn on the Auto Answer option (the default setting), the device automatically answers incoming calls and receives faxes after the number of rings that are specified by the Rings to Answer setting. (The default Rings to Answer setting is five rings.)
If you receive a legal-size fax and the device is not currently set to use legal-size paper, the device reduces the fax so that it fits on the paper that is loaded. If you have disabled the Automatic Reduction feature, the device prints the fax on two pages.
NOTE: If you are copying a document when a fax arrives, the fax is stored in the
device memory until the copying finishes. This can reduce the number of fax pages stored in memory.
This section contains the following topics:
• Receive a fax manually
• Set up backup fax reception
• Reprint received faxes from memory
• Poll to receive a fax
• Forward faxes to another number
• Set the paper size for received faxes
• Set automatic reduction for incoming faxes
• Block junk fax numbers
• Receive faxes to your computer (Fax to PC and Fax to Mac)
Receive a fax manually
When you are on the phone, the person you are speaking with can send you a fax while you are still connected. This is referred to as manual faxing. Use the instructions in this section to receive a manual fax.
NOTE: You can pick up the handset to talk or listen for fax tones.
You can receive faxes manually from a phone that is:
• Directly connected to the device (on the 2-EXT port)
• On the same phone line, but not directly connected to the device
NOTE: The automatic document feeder must be empty to receive a fax. If there are documents in the ADF, then the device will not be able to receive incoming faxes.
To receive a fax manually
1. Make sure the device is turned on and you have paper loaded in the input tray.
2. Remove any originals from the document feeder tray.
NOTE: The automatic document feeder must be empty to receive a fax. If there
are documents in the document feeder, then receiving the fax will be
unsuccessful.
3. Do one of the following to answer a fax manually:
• Set the Rings to Answer setting to a high number to allow you to answer the
incoming call before the device answers.
• Turn off the Auto Answer setting so that the device does not automatically
answer incoming calls.
4. If you are currently on the phone with the sender, instruct the sender to press Start on their fax machine.
5. When you hear fax tones from a sending fax machine, do the following:
a. Press START FAX Black or START FAX Color on the device control panel.
b. When prompted, select Fax Receive.
NOTE: Depending on your country/region, the device might receive the fax
automatically when you hear fax tones from the sending fax machine.
6. After the device begins to receive the fax, you can hang up the phone or remain on the line. The phone line is silent during fax transmission.

Can you still send fax? if sending and receiving are not working you can try to update or uninstall/reinstall the software for this unit..

Hope that helps.............

You do not give enough information. What happens when you try to receive? Does it ring? Is there any message displayed?

You will have to look through the options in the unit to find the receive settings in the menu. Make sure it's actually set up to receive. Usually there are receive (RX) options such as: manual, fax/tel, fax only, number of rings, distinctive ring and others.

In most cases if the machine is set to manual, you will have to press a button to receive a fax. It may be just the "hook" button, or a start button. Check your owners manual to see which button. In Fax/Tel mode the machine will assume you are using a telephone on the same line. You will have to set the unit to answer after the phone rings a specific number of times(four, for example). After four rings, if you have not picked up the receiver the machine will take the like and receive a fax. If you set it to Fax Only you can set it to answer on any number of rings, but it's best to just set it to one. In this mode the machine assumes it has a dedicated line.

If you have distinctive rings for various people in your home or business then you will have to consult your manual to see how to deal with the different rings.

One last note. Make sure your phone line is plugged into the correct port on the machine. I get a ton of calls at work from people who have the phone line plugged into the extension port, and the phone plugged into the line port.

If none of this helps, you will need someone to look at your fax machine. If you call HP, have your credit card ready.....

Go to menu option and choose the option fax and set the parameter like auto receive or manual set the ring auto answer mode after certain ring. If it is in auto receiving mode it will receive the fax after the ring which you set.
Have a nice day and do not forget to rate please...!

While it is ringing press the START button. You are set to MANUAL RECEIVE

You are set for MANUAL RECEIVE, when the fax rings, press the START button to receive a fax.

Check the MENUS for AUTO RECEIVE settings.

Receive Mode Settings Select from the following receive mode options to suit your needs. Once you've decided on which receive mode to use, follow the below instructions to set the receive mode using the operation panel. Receive Mode Setting

1. Press the <FAX> button to enter Fax mode.
   
2. Press <Menu>.
   
3. Press the right or left arrow button to select [Receive mode settings], then press the <OK> button.
   
4. Press the up or down arrow to select the receive mode that best suits your needs, then press <OK>.
   
   

Types of receive mode
Select the receive mode according to your needs.
Receive mode
Purpose
FAX/TEL AUTO SW When you want to receive faxes automatically as well as voice calls. FAX ONLY MODE When you want to receive only faxes automatically with your machine, or have a dedicated telephone line for FAX use only. DRPD When you have subscribed to a DRPD service with your telephone company. MANUAL MODE When you receive mainly voice calls and sometimes faxes, or want to receive faxes manually. ANS.MACHINE MODE When you want to receive voice messages on your answering machine and receive faxes automatically. FAX/TEL auto switch
FAX :
The machine does not ring but will receive the fax automatically. Voice call :
The phone attached to the machine will ring. Pick up the handset to answer the call. Note:

• Ring start timing and Telephone ring length can be specified in FAX/TEL auto switch in the Receive mode settings.
  
• If you want the telephone to ring when it receives a fax, connect a telephone to your machine and enable the Incoming ring settings in RX settings.
  
• The phone attached to the machine may not ring depending on the telephone type you are using.

FAX only
FAX * :
The telephone does not ring. The machine will receive the fax automatically. Voice call :
You will not be able to answer the call. * If you want the telephone to ring, connect the telephone to your machine and enable the Incoming ring settings in RX settings menu.


DRPD
FAX :
Your telephone line will ring according to the ring pattern you have chosen and receive the fax automatically. Voice call :
Your telephone line will ring according to the ring pattern you have chosen. Pick up the handset to answer the call. Note: Specify the FAX pattern in the DRPD: Set FAX ring pat. in RX settings menu.

Manual RX
FAX :
The telephone attached to the machine will ring. Pick up the handset and if you hear a beep tone, press the <Color> or <Black> button on the machine to receive the fax. Voice call :
The telephone attached to the machine will ring. Pick up the handset to answer the call. Note: If you are far from your machine, you can use the remote receiving function to receive faxes. Pick up the handset of the telephone connected to the machine and press 25 (the remote receiving ID).

Ans. machine connect
FAX :
First the answering machine connected to your machine will respond to an incoming call, and then the machine will receive faxes automatically. Voice call :
The answering machine connected to your machine will respond to an incoming call. Note:

• Set the answering machine to answer on the first or second ring.
  
• The entire message should be no longer than 15
  

Set your fax machine for AUTO RECEIVE. Unplug power cord and plug back in.

To select or change your Receive Mode
1 If it is not illuminated in green, press (Fax).
2 Press Menu/Set, 0, 1.
3 Press ▲ or ▼ to select Fax Only,
Fax/Tel, External TAD or
Manual.
Press Menu/Set.
4 Press Stop/Exit.
Setting the Ring Delay
The Ring Delay sets the number of times the MFC rings before it
answers in Fax Only or Fax/Tel mode. If you have extension
phones on the same line as the MFC or subscribe to the telephone
company’s Distinctive Ring service, keep the Ring Delay setting of 4.
(See Operation from extension telephones on page A-7 and Easy
Receive on page 4-4.)
1 If it is not illuminated in green, press (Fax).
2 Press Menu/Set, 2, 1, 1.
3 Press ▲ or ▼ to select how many
times the line rings before the MFC
answers (00, 01, 02, 03 or 04).
Press Menu/Set.
(If you select 00, the line won’t ring at all.)
4 Press Stop/Exit.
Initial Setup
1.Receive Mode
Current Receive Mode
Fax : Fax Only
F/T : Fax/Tel
TAD : External TAD
Mnl : Manual
Setup Receive
1.Ring Delay

check the manual


http://www.retrevo.com/s/hp+1040+manual


go to page 28 setting with a caller ID