Just wanted to say that I solved the thing. I reinstalled the Fedora but this time I didn't use NVIDIA drivers. My only concern wasn't some lack of high 3D power but just the resolution. On System -> Preferences -> Hardware -> Screen Resolution there weren't no 1024x768 resolution. The highest was 800x600. Here's whata I did:
I updated system from System -> Administration -> System Update. I downloaded everything!
Then I donwloaded using yum from terminal 'system-config-display'.
It required some additional files so i downloaded them too. When I did all that, I restarted Fedora, and then from Terminal I typed command 'system-config-display'. You have to be root for this. Then it opened similar window like that in System Resolution one. But this had more options. In this too, the highest resolution was 800x600. But on some tabs there was info about Monitor and Graphic card. I opened info about Monitor and there it was to choose the resolution of the monitor. When I did this it asked me to restart X so I did just that. When X started it started in 120?x??? some resolution way higher than I wanted and also it showed some screen problems before it soon started. I opene System Resolution again and this time there was resolutions to choose from and I reduced from 12??x??? to 1024x768 which I wanted all the time. THERE. Everything works liek a charm now. Hope this post will help someone with the same problem like mine. I think this thread could be locked now.