Solution 1:

I've removed xserver-xorg-input-synaptics, unplugged the auxiliary mouse and restart the laptop.

The touchpad is recognised and the main functions working.

Thanks Pilot6 for the help.

Solution 2:

For my Lenovo IdeaPad 5 15IIL05 - i5-1035G1 Michael Reutman's (mreutman) solution in launchpad worked like a charm. I had to:

  1. Edit /etc/default/grub (with nano /etc/default/grub) and change the following line as shown:

    GRUB_CMDLINE_LINUX_DEFAULT="[...]"
    

    To

    GRUB_CMDLINE_LINUX_DEFAULT="i8042.nopnp=1 pci=nocrs quiet splash"
    
  2. Update GRUB:

    update-grub
    
  3. Reboot.