why not use the battery connectors for power and ground? you need any controls/buttons that were in the speaker in order to control the board. exactly what was connected to the connector circled in red?
disassembly tip: freeze mist (or a "canned air" can turned upside down) will make the red glue on the connectors brittle, making unplugging the connectors much easier. just drip the liquid onto the red glue so that it gets very cold. this makes the plastic connectors brittle too, but far less brittle than the red glue