I had this problem for several weeks, read forums including this one, none of the solutions fixed it for me. Then I tried something of my own, and it worked:
Go to Start Menu -> All Apps, right click on any program, and choose Open file location. Not all programs offer this option, hunt around and find one that does. It doesn't matter which program it is. This takes you to the Start Menu folder where all the Start Menu short cuts are.
Copy that entire Start Menu folder to somewhere outside the Windows system, just to back it up.
Delete the entire Start Menu folder from the system. You will be told you need permissions. Accept this, and continue with the deletion of the folder so that it is gone. If it goes to your trash, empty your trash. Get rid of it completely. Remember, you made a copy so you have what's in there.
Go to Task Manager, find Windows Explorer, right click, and Restart it. The screen will black out, then recover.
Go to the Start Menu. The system will rebuild it from scratch. The rebuilt version -- for me, at least -- works as it should and I can pin anything I want there. If you had shortcuts in your old Start Menu that you want to use, get them from the backup you made. Just right-click and select Pin to start.
I had my new personalized Start Menu looking exactly as I like it in about 10 minutes.