Is the time and date stamp on the computer 100% correct to your current time zone? One suggestion may be to try to right click on Fusion 360 and select the "Run As Administrator" option.
There won't be other start-up icons on the desktop or in the menu. Can you try to browse to the following location in Windows Explorer?
%localappdata%\Autodesk\webdeploy\production
or
C:\users\%userprofile%\appdata\local\autodesk\webdeploy\production
In this directory, there will be many folders with ID numbers that are specific to each version of Fusion 360.

Can you search these folder for Fusion360.exe and then try launching the application directly from the production folder?
If all else fails, it may help to go through the clean uninstall procedure in the below link.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/How...
After performing the clean uninstall, go to the below website and select Download Free Trial to being the re-install process.
http://www.autodesk.com/products/fusion-360/overview
I hope this helps. Let us know if you have any questions.
Thanks,
Nathan Chandler
Principal Specialist