This could happen for a few reasons. The typical reason is typically due to web browser misconfiguration. Hamachi will try to automatically use your web browser settings, but if it cannot, it will not be able to connect. Because the OS also uses these proxy settings, Hamachi will use the settings configured for Internet Explorer.
In Internet Explorer, go to Tools > Internet Options.
Click LAN Settings.
If everything in there is blank, set auto-detect on, and click OK on all the windows. If it is not blank, note the proxy settings, and then click OK on all the windows. If a proxy script is listed, you will need to get the proxy server information from your system/network administrator.
On the Hamachi client, go to System > Preferences > Settings.
If a script is used in IE, set the Automatically detect settings to Yes
Test your connection after this change by restarting Hamachi; if it fails, continue to the next option
If you need to manually enter the settings from IE, do so in the corresponding locations.