It sounds like Kali may have forgotten to include config_HID_RMI in their kernel configuration:
https://forums.gentoo.org/viewtopic-p-7782000.html?sid=31e7daf6e1755f1924ba0753b41f230f
To verify, you need to find the kernel config file. If the live USB works on another machine, or if you can connect an external keyboard to the laptop, run zcat /proc/config.gz | grep -i HID_RMI.
If you can't do this from a running Kali instance, you can find the config on the live USB image:
/boot/config
OR
/boot/config-$(uname -r)
This one is not compressed, so just run:
cat /boot/config | grep -i HID_RMI
OR
cat /boot/config-$(uname-r) | grep -i HID_RMI
If this is not the problem, then please post your Kali linux config.gz on a pastebin somewhere and paste the link here. Otherwise, the easiest follow up step is to boot with an external keyboard attached, install Kali, make sure the network is running, then follow the Kali linux instructions for installing and configuring the kernel sources:
http://docs.kali.org/development/recompiling-the-kali-linux-kernel
During the configuration step, turn on HID_RMI support. It is found under Device Drivers -> HID support -> HID bus support -> Special HID drivers.
Make sure you save the configuration before completing the remaining steps. Reboot the machine and verify that the keyboard is working and that everything is working properly.
The last step should be to file a bug report with Kali linux to make sure that other people don't have the same problem.