Sorry you are having trouble!
This can happen on a network that uses a firewall (like Fortigate) or other routing hardware that is doing "deep packet SSL inspection". Spine uses a self-signed, pinned SSL certificate to communicate with our servers and this can be rejected by some network configurations. It can make sense to block self-signed certificates for web browsing, but Spine's communication is different as a desktop application and a self-signed certificate makes sense because it needs to be long-lasting. Still, some default network configurations don't expect that and apply the rules for web browsers to everything. If that is the case, you'll need to configure your network to allow Spine's traffic.
Connecting to the Spine servers can also fail similarly to this error message on networks that have a "captive portal". Spine tries to connect, but the router serves up some HTML page (for example, for a login form for internet access) instead of communicating with the server.
Lastly, if your internet access requires a proxy, you'll need to run Spine from the command line to specify the proxy parameters:
http://esotericsoftware.com/spine-proxy-server
