The problem turned to be in the mixture of i586 kernel, mistakenly installed, and i686 kernel devel. That is why the compilation, which is done on the base of i686 source files cannot be installed in i586 kernel.
It is a FC bug, known to the Nvidia guys. I replaced i586 with i686 kernel files to match the source files (and my processor) and the driver was installed successfully.
I handled all text mode operations with disgust, but finally learned a lot about FC to help me arrange the several Linux machines in our company. Still wondering: why FC and NV guys do not pay more attention to such simple welfares like installing a graphic system from within a graphic environment. Having the distro CD/DVD should be enough to accomplish it without digging into the config jungle with vim!