I suspect there is a problem with your wiring.... CHECK ALL CONNECTIONS 3X BEFORE PITCHING THE AMP..... LOL !
have you checked that the RCA's are both working ? I remember having the same problem back in the day; and thats what it was... (noob me didn't know to check things like that back then

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anyway, the speakers working in turn with the bridge switch has to do with the how the inputs and outputs are setup... check it out and let us know what happens....