I can send a fax, but not receive one.

You need to configure your fax machine to act the way you want it to. instructions will be in the owners mmanual ..

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.

Introduction The HP All-in-One can receive faxes automatically or manually depending on the Auto Answer setting. If the Auto Answer option is set to On (the default setting), the 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). Refer to the given instructions to receive faxes automatically or manually. Receiving faxes The HP All-in-One can receive faxes automatically or manually. Receiving a fax automatically To receive faxes automatically, set the Auto Answer option to On (the default setting). The 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). Receiving a fax manually If the HP All-in-One has been set up to receive faxes manually (the Auto Answer option is set to Off ), or you answer the phone and hear fax tones, use these instructions to receive faxes.

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. Set the Rings to Answer setting to a high number to allow you to answer the incoming call before the HP All-in-One answers. Or, turn off the Auto Answer setting so that the HP All-in-One 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:
   1. Press Start Fax Black or Start Fax Color on the control panel of the HP All-in- One.
   2. When prompted, press the down arrow to highlight Receive Fax Manually , and then press OK .
6. Press Start Fax Black again.
7. After the HP All-in-One begins to receive the fax, you can hang up the phone or remain on the line. The phone line is silent during fax transmission.
   
   
   Trust this is helpful. Please vote. :)
   
   

Problem lies in your Receive Mode setting. If you don't have a dedicated phone line for the fax machine, you need to set it up for either Manual where you answer every call or Fax/Tel whereby the Fax machine determines if the incoming call is a fax or phone call. Instructions per Intellifax 4100 Manual.

Select a Receive Mode
Choose the mode that best suits your needs by pressing the Mode button
repeatedly until the FAX and FAX/TEL lights show the setting you want to use.
Manual
You must answer every call yourself.
The Brother machine must be started manually
to receive faxes.
Fax
For use with a dedicated fax line.
Every call is answered as a fax.
Fax/Tel
For receiving fax and voice calls on one line.
The FAX answers every call and receives a fax or
double rings for you to pick up a voice call.
TAD
For use with an answering device.
The TAD answers every call and stores voice messages.
Fax messages are printed.

First thing to check is the condition of the phone line, if the machine has a handset make a phone call from the handset, is the line clear? Is there any static or Echos on the line?
Is the machine on a shared line with computers or an answering machine?
Call the Fax machine from a phone, is the line clear? did the machine generate its handshake burst? Did anything else try to answer the line?
Check the phone cable input, it should be going onto the LINE jack on the back of the machine.

What is the make and model?

Call the fax machine from a regular phone to see if it answers.

I think you have some sort of phone line problem.

Fax machine modems are good or bad, nothing in-between.

After making my post, I went to the official Brothers website for the 4100 FAQs and "Operating Instructions." Here's what I found. Set your 4100 set to the "Fax/Tel" mode. Press "Menu", then the number 2 (Fax), then number 1(Set-up Receive), then number 1 again (Ring Delay). Use right arrow key to increase. Once increased, press the "Set" key. You'll see the message "Accepted." Now press the "Stop" key to exit "Menu." This will now give you up to 4 rings before the fax auto answers. Inorder to send a signal by phone to remote start the fax just follow the instructions I copied directly from Brothers instructions for the 4100: If you answer the call on an extension phone (this is any phone plug into a phone jack on the same line) and hear a beep every 3 seconds (automatic fax) or just silence (manual fax), press *51(remote activation code) on the telephone keypad, wait to hear the Brother machine turn on (chirping sounds) and then hang up. I don't have anyone that can send me a fax right now to test it out. I'll have to try it in the morning. Hope this works for you.
THEOH

Send will work on any phone lines
fax machines are often set to only answer 'secondary' ring tones, double triple or higher. When the line was repaired the phone company may have dropped the special tone off your secondary fax line number, fax will not answer without that tone.
Check in the fax answer settings, what the ring tone is, specific instruction on menu settings in your user guide,
Ring your fax line, and check the tone.
If single number fax/phone, check that the fax is set to asnwer all calls then pass on non faxes

You should verify two things:

1. Is the phone line from the wall plugged into the correct jack on the fax machine. It should be in the one marked as "Line" or "L", NOT the one with the picture of a telephone or the letters"ext".
2. Is the machine set to automatically receive faxes. These have different modes of reception. "Manual" receive is when the fax will not answer the incoming call unless you tell it to. This is for users who have an answering machine or phone hooked to the same line as their fax. "Auto" receive is when the fax answers the incoming call automatically after a certain number of rings.

If you only have the fax on this line, your fax should be set to auto receive. If you need instruction on how to set that feature, please let me know what the model number is and I'd be happy to provide that info.

If neither of these seem to be your problem, trying testing the phone line with a regular phone to insure there are no line issues.

Hope this helps!

Just found your post and I'm having the same problem. Everything else seems to be working correctly. I can copy, scan, print and I THINK I can send a fax correctly, I should have called the person and made sure it arrived. However, I cannot receive faxes. I have an answering machine on the line, but it is not plugged into the Kodak Pinter, it is in another room. The answering machine answered the call, the FAX noise came across, but the Kodak Printer never picked it up and printed out the fax. I think I have all the settings correct, but the instructions are not very clear. Do you think I HAVE to have the answering machine plugged into the Kodak Printer? That doesn't make sense, but I might try it.