Does the following link show your speakers?
https://www.adorama.com/ggbp000100bk.html
It could be the output port from the subwoofer but there are some other things to try:
First what is the audio source when you are
not using headphones - is the source the same source used for the headphones or another source?
If a different source verify that that source is sending out an audio signal. Look for any volume controls (hardware or software) on that source device. Windows 10, for example, has quite a number of audio related windows, tabs, and properties settings.
Second, try another known working audio cable between the audio source and GoGroove. Be sure that the plug(s) is/are being fully and firmly inserted.
Third, inspect the cables. Ensure that the cables are correctly pinned and undamaged. Especially around the plugs.
There are different audio plugs and you also need to ensure that the correct connection cable is being used.
Reference:
https://www.cablechick.com.au/blog/understanding-trrs-and-audio-jacks/