What color is the LED when you power on the speaker? Have you tried a factory reset? 
If it still does not prompt you to add the speaker after you reset it, I would suggest giving Sonos support a call. 

Maybe borrow or buy a cable? If you avoid the folks gouging on price they are cheap.

https://www.amazon.com/Amazon-Basics-Ethernet-High-Speed-Snagless/dp/B089MGH8W3/ref=sr_1_1