Hi twar, welcome.
In addition to TVeblen's advice, try right clicking on the shortcut, choose properties, choose Shortcut tab to get the 'path' of the file (as seen in screenshot). You can try clicking on the 'Open file location' button, but it may not have any effect.
In Windows Explorer, browse to the folder specified in the 'Start In' field. Try this with a number of the shortcuts you have. Are the folders there? Do you see the .exe files in the folder?
If the folders and exe files are
there, you may have picked up a virus or malware. You can download the free version of malwarebytes here: Malwarebytes' Anti-Malware: Malwarebytes
If you don't have a virus program, you can download the free MSE (Microsoft Security Essentials) here: http://www.microsoft.com/security_essentials/
Do a full scan in both (one at a time). If it is indeed a virus or malware, allow the respective programs to clean up the system. If an infection is found and your exe files still don't work, you may have to repair the associations, but we can cross that bridge as it comes.
Follow TVeblen's advice first, then follow the steps in this post. Please post back when you have resolved the problem so that others may benefit from your experience.