Thanks Ira L.
I did check the Trackpad settings over and over but to no avail.
This is what I found under Finder Help:

In the Finder
If the item is on the desktop or in a Finder window, double-click it.
If the item is in the Dock, or in a Finder window sidebar or toolbar, single-click it.


The single-click works just fine for items in the Dock, except for the double-click of desktop folders and folders within folders which are not responding.
I remember the double-click was responding when I first got the MacBook Pro
till 2 days ago.