Before assuming the problem is with the fax make sure that your phone line is working and that the phone cable is working and plugged in securely. The easiest way to test them is to plug the phone cable into a known working phone. If you have a dial tone press a number on the keypad and listen to the line. It should be free of hum and crackling.
If you've done the above test and everything seems okay, then the fax module is probably the source of your problem. I'm fairly certain that it is separate from the main electronics board. Unfortunately HP does not sell the module or reveal it's part number (P/N). Perhaps someone on the forum has the P/N. Once you have the P/N there is a possibility of finding a used part seller that has it in stock.
