Kamal, I checked and there are some errors, but apparently all related to my CMS (Drupal), not to nginx.
Gavin, I haven't installed any firewall (at least not consciously).
Dave, I don't fully understand what you say (I'm very new to nginx and to sysadmin issues in general) but I think that could be the problem or at least related to that:
I have several domains in the same nginx server and therefore several "server declarations" in the same configuration file (all included in /etc/nginx/sites-available/mysite). When I put listen 8080; in the first server declaration (save and restart nginx) and go to that first domain, it redirects to the next domain in the nginx configuration file.
Simplifying, it's something like this:
With this configuration, when I open www.domain1.com in my browser it redirects me to www.domain2.com. That could be related to what you were talking about? That gives more clues about what could be my problem?
Thanks again for all your quick responses!