The screenshots revealed the issue is different from what I was thinking the issue was. There does not appear to be any certificate issue with our website, as far as I can tell. The log file that you uploaded last, which is the installation log file, doesn't reveal any problems. It confirms the current release of Fusion 360 was successfully installed.
If at all possible, could you look for the application log files (different log files) stored in:
C:\Users\<USERNAME>\AppData\Local\Autodesk\Autodesk Fusion 360\<ID\logs.
If you can share the latest application log file with me, it may help to reveal more about the error.
There are a couple of suggestions below that may help if this is a network connection issue. Please keep in mind these are blind guesses, but they have proven helpful in previous cases.
Reset the Internet Options (Windows Only):
1.
Clear the browser cache (CTRL + SHIFT + DELETE while in web browser) 2. Browse to
Control Panel\All Control Panel Items\Internet Options 3. In the
Advanced tab, select the
Reset button to reset Internet Explorer's settings to the defaults
4. In the
Security tab, select
Reset All Zones to Default level
5. In the
Content tab, select
Clear SSL state 6. Select
Apply Note: In the Advanced tab, it may be helpful to note if the options for SSL and TLS are enabled.

Check the Automatically Detect Proxy Server Settings:
1. Browse to Control Panel\All Control Panel Items\Internet Options
2. In the Connections tab, select LAN settings
3. Try to Enable/Disable a Automatically detect settings option
3. Apply the changes and retest.
If none of this is working, it may be worthwhile to perform a manual clean uninstall of Fusion 360 and then re-install the program from the Autodesk Website (select download free trial to get started).
I hope these suggestions help. Please keep me posted on your progress. I'm interested to learn more about this issue.
Thanks,
Nathan Chandler
Principal Specialist