First of all, I have a perfectly working installation of nginx / PHP / fastcgi on the latest stable Debian distribution. No problems at all, apart from this one:

When a PHP script (script A) is written to request a PHP script on the same web server (script B), nginx takes several minutes to respond and finally the connection times out. And it happens only when invoking script A through nginx. Calling it from command line works fine — I get a normal output of script B.

Literally, the test case is as simple as:

Script A:
Script B:
I suppose the root of the problem may be some obstacle occurring when php5-cgi ends up invoking itself. And this is what happens when script A is called through nginx. But I have no ideas yet how to address the problem.

One of my PHP applications checks itself during installation, that's why I need to request a PHP script from a PHP script on the same server.

I'd say it's something with the firewall... if active.
Idea:
Command line goes through loopback which normaly is allowed by every firewall
nginx goes with the ip the http server is listening on. And this could be blocked by the firewall.

Or you just have a simple dns issue, which I somehow doubt.
Does the server give out any further error message? Maybe you can use gethostbyname to see if php does dns right.