Just in case anyone encounters similar problem, I managed to locate the issue to the MBPs trackpad. While it reacted to finger movement, it did not react to clicking (pressing it down). I got my monther in law to connect a USB mouse, at which point she was able to click on her user circle, fill in the password and log in. Then we disconnected the USB mouse and the trackapd worked just fine. No idea what was the real problem but at least it works now.
Still, any tips are very much welcomed.