I'm putting this up in case it will help anyone else.
Running Windows 10 but I don't think this fix will be OS dependent.
I have had two PC in the last couple of weeks that Dropbox has stopped syncing on, saying there is no internet connection (there is).
I spent hours trying to fix it and did everything short of reinstalling Windows
I ticked the 'no proxy' box but the setting wouldn't stick, just reverted when I restarted Dropbox
Turned off the firewall
Reset the firewall
Reset everything in Windows using tweaking.com using all of the fixes
Created a new user to see if it worked for them
Ran the netsh winsock reset catalog command
Uninstalled Dropbox completely and reinstalled it (had to use the offline installer as it wouldn't connect to the internet for the online one)
and a whole bunch more stuff that I can't even remember
Anyway what fixed it for me, and I've not seen this fix anywhere in my extensive searches it was just a last throw of the dice, was to change my DNS servers to Google's so in the internet adapter properties options choose 'use the following DNS server addresses' and put Google's in there
Both these computers were on the same network connected to the same ISP and are in Hong Kong so I did wonder if it's a Chinese Government thing, then I took my tinfoil hat off and decided it is more likely just an ISP mis-configuration.
Anyway if you have the no connection problem and you've tried everything else then give it a go.