Time for 2 replacement phones! To prove this for sure, temporarily swap positions with a working location. If the problem 'moves' with the phone, then it's the phone. If the problem 'stays' at the location, you have other problems.
Then there is the problem that the 944 is loonnnggg out of production.
Do a search in the forum for 944, somebody outlined what AT&T 4-line phone work together. They don't all work together and the 944 is the real problem, if I recall correctly.
Check this thread in this same forum. At&T 944 Phone