Have you tried to update the firmware? That might recover the board from its current state. I recommend you to download the Firmware Updater Tool and try to update the firmware: Download Intel® Galileo Firmware and Drivers 1.0.4.
Although you have updated the firmware before, I still recommend you to use the Firmware Updater Tool. The firmware might have gotten corrupted, and updating the firmware might recover the board.
Additionally, are you powering the board through a DC power supply? I cannot see it in your picture. Also, did you try to power on the board without the SD Yocto image to check if the same issue is still happening regardless if you are booting from the SD Yocto image or not? Do you have access to the terminal of the board?
Have you tried to access the boards' terminal through the FTDI cable? ==>> Not yet
Additionally, does the behavior change if you power up the board without the SD card? ==>> No
How are you powering the board? ==>> Plug Power first then wait for USB led but USB never goes on.
Are you using the DC power supply? ==>> Of course.
Is the board getting hot?
Let’s try with the FTDI cable (remember to use a 3.3V cable), with this we could check if the board is booting.
Also, have you tried to connect the board to another PC, the problem could be related to the current in the ports.
Are you using 2.0 or 3.0 USB ports?