No they dont have relays from the factory. Hmm sensitivity adjust???? How big is this box, if its small that sounds to me like a dual proximity sensor (someones obviously splashed out), or it could be the main unit but the main unit is quite big.

If you look the window feeds i would of thought would be fused, whip the fuses out and see if that makes any difference, (if theyre not thats a bit shit).

Yeah the relays apply power to certain wires in order to raise the windiws. Pictures would probably be good