I have downloaded the latest version of Unity,but whenever I try to open it, it shows an error displaying “Error connecting to license server”, although I always have internet connection while opening it. Does anyone know how to get over this problem? Please !!!
You could try as StaticHS said and disable anything that could be blocking access to the license server.
Alternatively you could use the manual activation process:
If everything you try fails, Send an e-mail to support@unity3d.com and they will be able to help out and get you running 
fixed: when you get the 500 error code just hit F5 to refresh. you will eventually get through the steps.