If I use PHP 5.3 everything works fine.
When I switch to PHP 5.4 then the site works only if I turn off W3TC.
Behavior with PHP 5.4:
-The site appears without CSS / just text and images (broken site)
-If I try to open the site and see the source code I can see the minified css link - I click on it and I get a 503 error;
-If I disable in the wp-admin the minify and refresh the site, I still can see the minified files added by W3TC - so the plugin does not turn off the minify with PHP 5.4 on.
-Everything starts to work back again if I disaple W3TC OR I go back to PHP 5.3.