I just started having this problem today. I use a VPN then VNC to my work computer. I have been connecting like this without problem for years.
Screen Sharing opens and appear like its trying to connect, but just sits like that. Normally, when it can't connect I get a message saying so. Nothing.
I did try all the fixes above, rebooting, checking the activity monitor for NetAuthAgent - not there.
I can AFP and SSH no problem. But, I have a ton of work to do and really need to see my screen.
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Go to System Preferences. Then "iCloud".
Do you see your Apple ID in there, without the password?
Delete the Apple ID, and then close that System Preferences window.
Now try screen sharing again..