Quote Hugh Robjohns:
The currents that flow in the building's ground wiring are perfectly normal, safe and expected and these currents will inherently cause a voltage to develop across that wiring because the wiring itself has a finite resistance. The equipment in different rooms will therefore 'see' slightly different ground reference voltages, and that will cause a 'ground loop current' to flow along the audio cable screens between them.
Slightly different ground reference voltages = no unity!
OK, I learnt this stuff in a different country and the way I understand things, a unified earth is unified when and only when the earth does not rely on the earth wire alone for its unity. If there is a difference between two parts of the building's earth, then it cannot, by definition, be unified. The very structure of the building and the ground it sits upon have to provide the unity.
The problem with giving answers to questions on a forum, is that one assumes too much or too little. In this case, I am assuming that the OP has done everything as he should, in particular, bearing in mind input impedance and the effects of long cable runs.