Typically this happens due to web browser misconfiguration. LogMeIn 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, LogMeIn Hamachi will use the settings configured for Internet Explorer.

1. In Internet Explorer, go to Tools > Internet Options.
2. Select Connections.
3. Select LAN Settings.

If everything in there is blank, set auto-detect on, and select OK on all the windows. If it is not blank, note the proxy settings, and then select 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 LogMeIn Hamachi client, go to System > Preferences > Settings. Go to Advanced settings and set the Automatically detect settings option to Yes. Test your connection after this change by restarting LogMeIn Hamachi.