To clarify my earlier comment, I was not addressing the possibility that the two connections for one channel are interchanged, as the post by Tanathen78 earlier in the thread had already addressed that. As he indicated, that would result in the two channels being out of phase with each other, which would be perceived as vague and diffuse imaging, and probably also as reduced bass (which in turn might contribute to a perception of reduced volume).
What I was addressing was the possibility that the + wire of one channel might be interchanged with the - wire of the OTHER channel. In other words red interchanged with blue, OR white interchanged with green.
That would result in the center pins of the preamp's RCA inputs for the two channels being connected to each other through one of the cartridge's two coils, with both inputs "floating" (i.e., having no definable voltage or impedance) relative to the preamp's ground.
I don't know what the resulting sonic consequences would be, as they most likely would be dependent on the design of the particular phono stage. But it's certainly safe to say that the sound would be far from normal, and it seems quite conceivable to me that the result could be the very weak volume you have described.
I'm hesitant to suggest that you intentionally introduce that kind of reversal as an experiment, however, because another possible consequence that is conceivable to me would be a loud and potentially destructive hum or oscillation (although being careful with the volume control would PROBABLY eliminate any possibility of harm). That is one reason I suggested checking all of the wiring with a multimeter instead. Hopefully the shop will now do that for you.
Regards,
-- Al