OK, you have pushpins visible and it still won't add new ones. I am not sure it matters but did you do a "Show all pushpin sets" or did you go through each set and do "Show pushpin set"? Whichever you did, I would now try the opposite.
Looking closely at the cursor when dropping the pushpin onto the map, does it do a little splash, or starburst, as it converts the cursor icon from your selected pushpin to the default arrow? It does that for me if I create a new pushpin that gets added to a hidden set.
If none of the above, how would you feel about sharing the file, either broadcast on the Forum or as a PM attachment to Marvin or Larry? Their vast experience might help.