Polarity issues are so easily analyzed, after all, there's only two ways a pair can be terminated.
Polarity can also be inadvertently reversed, by using different manufacturers' jacks and cords. Remember, an "RJ11" or "RJ14" type cord is supposed to have a natural reversal built in, but I have encountered off-shore cords that do not reverse the pairs. I have a pile of them here that I bought for about a penny apiece on Ebay.
However, getting back to this mind-numbing thread, it seems incredible to me that a smart, educated, IT person cannot figure out the simplest polarity problem, if that's what's causing this.
Step one: find the last place along the circuit that the phone works correctly.
Step two: extend the pair to the next point and test again.
My goodness, it's like trying to get water to run down hill. It's not rocket surgery, gentlemen.