Yeah, that won't be necessary anymore.
What I did, was finally managed to go to save mode by:
.From the Windows Start menu, click Run.
.In the Open field, type MSCONFIG and click Ok.
.On the BOOT.INI tab, check /SAFEBOOT.
.Click Restart when prompted.
While I was in the safe mode, I actually couldn't even install new drivers but after few restarts I went back to Normal Mode and guess what. The Windows booted normally. But I downloaded all the newest drivers from ati site and installed them right away and rebooted. It all works. I suspect that screen resolution must've messed up something, because that is the only things that has changed during the process.
It works nice, I will be testing it soon in some demanding games.
Another things slightly ir/relevant to the topic (because it's software issue more).
There is this "Speccy" program by Piriform (maker of CCleaner), and the thing is, Speccy doesn't recognize the new card. According to Speccy I'm using integrated ATI 3200. According to "little info" from CCleaner HD5770 is in use, and so does windows display options and ATI Catalyst says as well. Would that be a minor issue with computer having trouble reading the card or is it just Speccy fooling with me?
Anyways thanks for the brainstorming here, I nominate this topic as solved