Finally I got it working...
I post the answer here to be helpful for future users.
The problem was in the hosts server file. As @Amenadiel told me in a comment, it wasn't resolving the names.
I changed the hosts files and it seems it took more than I expected (I made the changes 3 days before and they weren't applied yet) so I discarded the hosts issues as an option. But it seems it was the only problem.
Why, then, didn't work neither when I tried to reach it using its IP? Well, it's because of the server nature. It's a server hosted in the Cloud, so it will be - for sure - a Virtual Machine.
It has a public IP (the one I was pointing to) and a private LAN IP. The server could not see the public IP, so if I was about to use one, it should have been the private (LAN) one.
Thanks again to all of you for your answers and your patience with this server side newbie!