There is a Security Update for Windows 7 that apparently breaks the game. When you click on the icon, the cursor ‘spins’, but you never receive the Freelancer splash screen / intro.

I went through all my recent updates that were applied just before the game broke. I narrowed it down to the Security Update KB3086255 - which is related to the system’s graphics:

https://support.microsoft.com/en-us/kb/3086255

Hope this helps somebody else, but it drove me nuts figuring it out.