Once, my camera would not power down via Solo or front power button...I removed the camera battery and it then worked fine. Have you tried that?
For reference...on mine: with the camera in gimbal, HDMI cable plugged in, camera turned OFF...then Solo powered up, Solo LEDs turn front white, rear red, gimbal will align itself, rear gimbal light slow flashes green and all appears ready to fly...screen of camera is blank (camera has no power). I then power down Solo, the gimbal will go limp and all LEDs turn OFF.
If I do exact same procedure as above with HDMI cable unplugged from camera...I get exact same behavior.
I know if you power Solo up with no camera in the gimbal, the gimbal will try for a few seconds to align...then give up trying, and go limp...which is what yours is doing. That kinda implies that you have some issue with the connection between the large port on the rear of the camera making proper connection the connector on the gimbal. Check those ports for debris...and be sure you have the camera seated firmly in the gimbal and in that port.
There are really only a limited number of things you try/check before calling it "broken" and it has to be sent back. That would be cable connections, gimbal data cable in to motherboard, gimbal HDMI cable in to gimbal board, gimbal HDMI cable in to camera.