So my amazon Echo (1st) Generation device was working fine, but all of a sudden started spinning the blue ring of death light one day. After trying a lot of things, I thought it was dead too, however I was able to get it running again, and it's now working like new again.
Here's what I did:
1) Get a paper clip, and Reset your echo device by placing the paper clip in the small hole in the bottom of your 1st Gen Echo. When it's reset, you should see an Orange light briefly on the top ring.
2) Bring up the Alexa app on your phone.
3) If your Echo was previously Registered in the Alexa app, you may need to De-Register it first.
4) Add a new Echo device in the Alexa app
5) Go through the steps, it may not recognize the Echo. If that's the case, Turn OFF bluetooth on your phone, and try again.
6) With Bluetooth turned off, add a new Echo device and go through the steps. Even if it doesn't recongnize it at first continue to try, and eventually the Alexa app will try to connect to your Echo using WiFi. The Alexa app, will prompt you to change your WiFi to the "Amazon-XXXX" WiFi, and the Echo will start to connect. Continue to go through the Alexa app setup steps.
Hopefully, after a few minutes the setup will work and your Echo will be working again, and you will no longer have a blue ring of death light.
Keep in mind, I also restarted my modem and WiFi router, before going through the steps above and made sure that my WiFi was working correctly before Resetting my Echo, but I'm not sure if that's necessary or not.
Note: I've read some people got there Echo to work by getting a new Amazon Echo Power Adapter. But for only $20 more you can buy a new Echo (1st) Generation device, so I might just get a new device if I wasn't sure if it was the Echo or power adapter that went bad.