Yes. Anytime you are dealing with a problem at that most basic level (BIOS boot) then performing the CLRTC will eliminate a BIOS corruption as a cause.
I am assuming the keyboard is a USB or PS2 (wired) keyboard? If it is USB connected then try a different USB port.
The keyboard "driver
" is hard coded into the BIOS instruction set. So a wired PS2 keyboard should always work on a standard PC when operating at the BIOS level. A USB keyboard will normally work on a modern motherboard with a USB controller in the BIOS instruction set.
What was the result when you disconnected all the hard drives?
With all drives disconnected can you get into the BIOS settings normally?
Does the keyboard work normally?
You really should test the system without the drives installed before you perform the CLRTC/ClearCMOS. Otherwise you might lose some important clues as to what is going on. The key is that you say this behavior started only after you installed the SSD. So that should be your first focus.
There is no danger in harming the system in doing one or the other first, it is just a matter of gathering more information.