The experienced behavior described, to me, is the behavior that can occur during an installation.
Depending on the hardware this can happen.
Detecting and removing a keylogger/malicious code is not the issue if the assumption is true. If an attacker is able get a keylogger running on the system during install you have larger problems that the detection and removal will not solve.
Explaining your situation better would help, checking your keyboard is fully functional, detected & working as you expect is something I would try to figure out in your case.
This is starting point in detecting, finding and removing a keylogger.