Replace keyboard and see if problem is solved. The keyboard itself might be messed up internally. When you press keys it sends a signal to a chip that takes in digital logic. If the chip that handles the digital logic is damaged for the path of upper case with combination of shift key = 1 and other alpha keys =1, then the output will be as if the shift key was held and no other key pressed to output the upper case.
Curious if you have caps lock key ON, if you will get all upper case characters or if only shift + alpha key causes issue of missing upper case characters?