The cheap low power speaker system has no sub-woofer. The little 4" speaker is a mid-woofer because it is too small to be a sub-woofer. The amplifier for the mid-woofer produces only 5W.
Can you trace where each wire was connected to through the connector? If not, you will need either a good schematic or find someone with the same device who is willing to trace the connections.
If you have the plug that was on the cable and if there are still some of the wires on the plug then you have some hope of possibly getting the connections correct. But if the plug is disposed of because it was damaged then there is very little chance of connecting the wires to the correct locations.
In addition, unless you have very good soldering and unsoldering skills, it is unlikely that the circuit board will be usable after the 9-position Din connector is unsoldered and removed. You will have a much better chance of making it work by getting a replacement 9 position DIN plug.
If you find out where the wires should be connected, you don't need to unsolder the DIN connector. Just solder the wires onto the connector pins on the back of the board.