Hello cfescalante, welcome to our community!
Yes, the blue and red LEDs are static and the fact that they are on since the start means that power is received by both the Pi and the Shake boards, so the issue is not there, luckily. The green led should blink every now and then, and if it doesn’t, then the issue may be centered around the OS, as you imagined.
I’m sure it’s a writing mishap, but you should format the card before unzipping the new Shake OS on it. Is the microSD card the one that you received with the Shake, or is it one that you have bought yourself?
Make sure, after formatting and unzipping, that the files are in the basic folder of the microSD card, and not contained in a folder themselves. Sometimes the unzipping process, instead of putting the files as they should, creates a folder in the microSD space and puts the OS inside, so please check that, after unzipping, there is a number of files inside the microSD card instead of a single folder.
Also, it may take up to 30 minutes for the Shake OS to be ready and operative, even if, usually, the average time is around 15 minutes.
I will add the microSD card burning instructions again for your convenience:
I followed the numbered list points to burn the files on my SD cards, and I have not used Etcher or similar software.