Cannot mine cobblestone - does not appear in inventory

If I start a new world I am able to collect logs and items such as mushrooms but when I try to mine cobblestone it does not appear in my inventory.

I have tried multiple locations and I have tried with and without a pickaxe and no cobblestone appears.

This problem DOES NOT appear in an ongoing game on our local LAN.

I do not have cheats enabled, I simply took the starting options presented and clicked on Create World.

This problem happened one time before when there was a game update and uninstalling/reinstalling DID NOT fix the problem.  Instead, I had to delete the majority of the registry entries for Minecraft and all possible files before the problem was resolved and I was able to start a world.

I uninstalled/reinstalled to ensure I have the latest hotfix and again selected all the basic options except that I changed to peaceful so that I could get a screenshot.  From the attached screenshot you can see that I have successfully collected logs but when I took out a block of cobblestone none appears in my inventory.

The strange thing is that if I go into the ongoing family game we have on our LAN everything works fine.