Why do we get busy signal for every fax we send?

SOURCE: Sending Faxes

This could be a cable fault. Get BT to do a line test for you (this is free). If that is OK, change the telephone cable. Perhaps this is on an extention cable? Remove it.

SOURCE: wont' send a fax

In my experience, anything plugged up to a phone line can be some of the most susceptible to electric discharge. Thunderstorms, power surges, brown out, all of these can cripple or kill a fax machine. When I saw this symptom on a fax, 9 times out of 10 it was caused by a power surge of some sort. The line error is most likely the machine's outgoing line has been zapped. The 775 (and it's father, the 770) are some of the most straightforward faxes I have dealt with when it comes to faxing. There is no internal setting that I am aware of that would inhibit the sending of faxes. I would double check the transmission report to make sure that the machine isn't doing something weird like adding extra digits to the numbers you are dialing. It would still be worth your time to try a few things, though. I would plug the fax into another phone jack using a different phone cord if available. Also try using the fax as a telephone, call a number and see if you can connect. If you can, make sure both parties can hear each other clearly. If you can not, the machine will need to be replaced.

SOURCE: Busy signal on sending and recieving

Did you plug a phone into the phone jack and see if there is a dial tone?
Thats the first place to start.
After that let me know, and I will give you more ideas.
Sounds like a phone line issue

SOURCE: not connecting to fax out

Do you have a DSL or other digital phone line?

SOURCE: we can send faxes but we can not receive faxes.

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.