Fax says "receive failed" - HP Photosmart 2610 All-In-One InkJet Printer

Press Setup Button on front panel of printer
Scroll to Fax Settings ( Or Advanced Fax Settings )
You will find ECM ( Error correction mode )
Turn it OFF

Try to receive Fax, IT should work

check telephone line

Your fax machine thinks everything is OK. If you can receive you can send.

call the failing fax number with a regular phone and listen for fax tones.

This is because some faxes don't have Error Correction Mode capabilities.

If there's a slight distortion on the line, the receiving machine (without ECM) receives a fax with some minor errors. And even though for a human eye the resulting fax page is perfectly readable, for the machine, that thinks only zeros and ones, there was an error detected in the data, and hence the trasmission failed.
Faxes with ECM when they detect an error, ask the sending fax to re-send the last portion of data, and this way can bring the transmission to a 100% successful end.

So the only thing you can do is ask your recipients to upgrade their fax machines to an ECM-capable model :)

menu #-1-9-3-4 it works

Printing irregularites on sent faxes are due to spots or a dirty scanner.
Spaces on received faxes are due to a dirty drum, corona wire, or a failing or improperly installed toner cartridge. A new cartridge should be gently shaken back and forth sideways prior to installation.

My office fax machine can receive the fax in the memory, but it does not print it.

Problems receiving could be any number of problems. The first item I would check it to make sure no other devices are on the same line as the fax modem, such as a fax machine. This can cause a problem for a fax modem to receive faxes when another line is being picked up and listened to at the same time.
http://www.getfaxing.com/forums

A manual for this unit is available here.

Faxes fail intermittently or with only one fax number

• If static is present on the phone line, fax communication may fail. Have the phone line checked and serviced by the telephone company (or have the other party check their line). Phone line quality is the most common reason for intermittent fax failures. Some older locations and buildings have inadequate phone system wiring.
• If you are trying to send a color fax and it fails, try sending the same machine a black and white fax. Normally the fax will detect that the other fax is not color capable and will offer you the option to send the fax as black and white but this might not always be the case. Do not send color faxes unless you know the other fax machine is capable of receiving color faxes.
• Check the phone cable from the wall jack to the fax. It should not be coiled or longer than necessary. Coiling the cable can cause cross talk or echo on the line. Signal strength and quality can be lost with long cables.
• Make sure the phone cable routing (and any cables not plugged into the same jack but sharing the same line) is not near any electrical appliances (electric motors, fans, kitchen appliances, or televisions). Many of these devices do not have sufficient electrical shielding and can induce electro-magnetic force (EMF) onto the phone line. Computers are usually shielded sufficiently and do not cause this problem.
• Do not use a call-waiting service on the same line connected to the fax machine. The click sound caused by an incoming call can cause the fax to fail.
• You can block certain faxes on some models. Verify that the telephone number of the sending fax is not blocked in the faxing software. This is usually located in the Fax History.