OK, I've answered my own question and now I feel really stupid not spotting the problem myself before asking for help.
Answer: - the left button of my mouse (Logitech Perfomance MX) has stopped working !
Hence, no response when I clicked or dragged. Everthing works fine with a different mouse, or after remapping "left click" to the right button of the Logitech. Interesting on how even the OSX Utilities screen and the Hardware Test rely on a (working) mouse to operate.
Apologies for wasting people's time.