This might seem obvious, but have you ruled out your speakers as the cause of the failure?
Have you tried the Amiga with all new cables & speakers?
Is there a Digital to analogue convertor between the Paula and the RCA outputs? I'm just thinking, if it's not the Paula, and not the jacks, cables or monitor, and not a software problem, then it must be something in between the Paula and the RCA jacks. Maybe a line-level pre-amp or D/A circuitry. Maybe just a dead capacitor or resistor or something. Anyway, it sounds like this Amiga can be fixed if you're willing to put out a little cash or effort.