Open terminal and write:

I did and it did not work buddy

Would not driver issue perhaps?

Can you tell me which driver use your keyboard on Windows? most pcs and laptops use the generic one, if you have something different, or if you have a "lights manager" driver like razer laptops for example, it could be the reason.

It worked when I pressed a key and stayed for a few seconds and hung up. I do not understand the reason it seems that it worked until then automatically. Because I was formatting for other versions of Windows and it worked even with formatted HD, do you understand me? After Deepin's installation he stopped.

And citing also that I updated the firmware by Vaio Update, should be this too: /

Some options for you to test... haha...
Option one: Try using xset led 1, xset led 2... till 32, because xset maybe gave another number to your keyboard.
Option two: go to SourceForge and download "vaio-control-center", thats the same utility you use on Windows. You must download it anyways.

If it doesn't installs, check if you have qt4-qmake installed, necessary to run the app.
Option Three: Type echo 1 | sudo tee /sys/devices/platform/sony-laptop/kbd_backlight to force turning on the lights and the same command but with echo 0 to turn it off. If you had to come to this option, and you want to enable light automaticaly at start up, open the terminal, type sudo gedit /etc/rc.local and put the same command words (the echo 1 command) in a line before exit 0 phrase.

You helped me a lot! Thank you for sharing your knowledge!

The command: echo 1 | sudo tee / sys / devices / platform / sony-laptop / kbd_backlight
solved

Thanks for the great help!

Please add on Facebook?

I only use facebook for personal things, but if you need help again don't doubt on sending private to me here on Deepin.