Checking for a physical 'disable cursor' switch near the trackpad or on the side (there is none).Connecting either mouse (old or new) to a different USB port.Testing the mouse on a different computer (it works fine).Disconnecting the mouse and reconnecting it.Pressing all function keys to re-enable the cursor (fn+F1.Turning it off and on again (a few times).What we've tried so far, after extensive googling and keyboard-only navigation as suggested below: Hoping someone can suggest a keyboard-only fix that we haven't tried. Most solutions online don't exactly match this issue, or suggest fixes that require the use of a cursor, so we're a bit stuck. The laptop does not have a touch screen, so we have no way of interacting with things normally. They usually use a wired USB mouse, but the trackpad is doing nothing as well. It's present at the login screen, and gone immediately after.
A family member has a laptop with Windows 10, and the cursor has completely vanished.