playbase - doesn't work off ethernet

Make sure WiFi is enabled..

First, when you wired the Playbase did you leave the option for “Disable Wi-Fi?” enabled?

There have been cases where the wireless card in the Playbase has failed and that would stop the Playbase from communicating wirelessly.

When wired, contact Sonos Support and a diagnostic from your system will confirm whether the wireless card is still functional or not.

What exactly is your issue?  At the moment you are citing an issue with Ethernet/wireless and setting up Alexa. Those are two different issues. Although the Ethernet/wireless is probably the most critical. Also, to be clear the Playbase doesn’t natively support Alexa as it requires an external Alexa device such as an Echo.

I think I’ve narrowed it down, but still not working . I am trying to get the Sonos playbase to connect to the wifi. When I go to settings in my Sonos application and try to find the network it won’t connect the playbase. I’ve tried hard reset of playbase but still won’t connect to the wifi 

Is your wifi set to enable the older standards the Playbase needs to connect?

https://support.sonos.com/en-us/article/supported-wifi-modes-and-security-standards-for-sonos-products

Is the Playbase a new acquisition? Either way, are you sure the wifi card works? Sonos support can advise you on that. 
Regarding Alexa (or other voice control) there’s no microphone on a Playbase so you’ll need a different control device. 

The Playbases had an issue with faulty Wifi cards as I understand it. I have one which developed this fault a year ago. I just used it anyway as it was wired to my bedroom TV anyway and had been previously set up when the Wifi card did work. I recently managed to hard wire it into a Wifi extender disc and it now shows again in the Sonos App. So it definitely had lost it’s ability to connect to Wifi and now will only show in the Sonos app when wired via Ethernet.

It could be that your Playbase also has a faulty Wifi card if it only works via Ethernet.