I had this issue a while ago before giving up but the issue:
I installed Kali successfully onto a laptop running an SSD. Whenever I rebooted after the install, there was an issue with the... how would I say, backlighting was non-existant. I was barely able to see anything on the screen. I could see that the screen was still there, the text was still there, but there was no light. I also noted that the light was fine while the PC/OS was booting. I figure it had to be a graphics issue (worked fine in a VM on the same device), but even if there is a driver issue, can it be fixed when I can't login to the OS being that there is no light. Only thing I can think is re-install, fix the issue then reboot after install.
EDIT: Addiditional info: Laptop is a Toshiba Satillite L755D according to the menu, the device has a Radeon HD 6520G graphics adapter.