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Ok, I know that here it's all about gog version but sadly gog version don't have PL language and my mom can't speek english so I'm stuck with cd version.

As the problem, everything working fine (compatibile mode) till the title screen with the four buttons. If I try to start a new scenario or click on the tutorial button, it just resets right back to the title screen. I remember having this problem long time ago on Windows Xp but don't remember how/if I fixed it.
Do you have either expansion pack installed?

Did you run the game as administrator?
Yes (Corkscrew Follies) and Yes.
Well, there is no patch for the Polish version of RCT other than the Loopy Landscapes-specific 1.20.013, which includes official Win2000 support, which could help with troubleshooting :/

If you're running Windows Vista or 7, disable Aero in the game's compatibility tab in the properties menu, and try setting the desktop colour to 16-bit: http://www.guidingtech.com/9914/change-from-16-bit-to-32-bit-color-windows-7/

If you're running Windows 8(.1) or 10, go to the compatibility tab in the properties menu and choose the 16-bit colour mode.

Disabling DPI in either case might also help.