All connections to the Dropbox service are done using a secure connection (SSL). If you get an error that says "Cannot establish a secure connection," it is probably due to one of the following reasons:
Your computer will compare your system date to the expiration date of our SSL certificate. If your system time is stuck in the past or so far in the future that it is outside of Dropbox's SSL certificate expiration date, a secure connection will not be established. This is easily corrected by changing your system time to the current date.
Dropbox uses standard internet ports (80 and 443) to transfer data. However, many firewalls and security software (such as antivirus programs) will proactively block unauthorized or unknown internet services. Add Dropbox to your proxy or firewall settings as an exception to connect to the Dropbox service.
Known issues with ESET Endpoint Security Solutions: According to ESET's website, this product currently has a conflict with Dropbox when SSL scanning is enabled. Possible workarounds are to exclude the Dropbox certificate within the "Ask about non-visited sites" mode, as well as to exclude dropbox.exe from protocol filtering as shown here.
Some external software programs will change your computer's default proxy settings when installed and may not alert you of this. Confirm that your proxy settings haven't changed and if you don't use a proxy setting, select the option for "No proxy".