When the Game directory listed in the profile you want to launch uses a directory junction created with 'mklink /j', it doesn't launch.
Instead it gives me this error:
"The game directory is invalid or inaccessible.
Error details: The system cannot find the file specified
Filename on disk: .minecraft
Path: C:\Users-user-\AppData\Roaming\.minecraft
Exists: directory"

How to replicate the error:
1 Launch a normal minecraft profile, and close it.
2 Rename the .minecreaft folder to something else, like 'minecraft1'
3 Use the following command in Command Prompt:
mklink /j C:\Users-user-\AppData\Roaming\.minecraft C:\Users-user-\AppData\Roaming\minecraft2
4 Launch the same profile again.