Need help with a Bose lifestyle 28 series 2 sub replacement, or whole sound upgrade

[mda99das]

https://www.bose.co.uk/en_gb/support/products/bose_home_theater_support/bose_5_speaker_home_theater_... I have a basic setup. I have a Toshiba 4k TV that is connected to my Virgin box.
I have a 5.1 Bose 28 Series II sound system.
The satellite speakers are all hard wired, and the control unit doesn't have HDMI and uses aux cables.

The control unit which contains the DVD player actually works, however without the subwoofer it is useless.
I was toying with the idea of finding a second hand subwoofer which will bring back life into my sound system, or is there another type of sound system that I can go for that will make use of my existing satellite speakers ?

Many thanks

[mda99das]

Forgot to add the Bose system has optical in, and the 360 box has optical out.

[goslow]

Would the existing system still do what you need/want if you got the sub-woofer working?

If so, repair the existing setup. There is a repair link from your link above

https://www.bose.co.uk/en_gb/support/self_service/service_and_repair_request.html

and Bose sub-woofer units on eBay seem to be listed from around £50 or £60-ish.

Your link also states the system is 2004 to 2006 vintage so integrating something new into the existing, to make use of the hard wired speakers, might not be that easy.