I'm sorry to hear of the power issues you've been having here and would be happy to advise you here.
There is no direct power button for the Acoustimass 300 bass module, and this unit would have an LED indicator if this is connected to power.
As you are not receiving the power indicator and you have already tried a different power cable and a different power port, my advise would be to reach out to Bose Service directly for service to your product. You can do this by selecting your country/region from the link, and navigating to "Contact Us" at the bottom of the page if required.
I hope this helps, and please return to me with any questions!