Okay, so how it has started. I have Win10 for nearly half year and Nvidia Geforce Experience all that time. Also I'm using built-in administrator (password protected to solve the issues with Windows Store etc.). And some time ago (maybe month or so) GFE started to show errors (basically "package can't be installed") instead of launching/updating itself. Fun thing that it can be installed with the driver package, but cannot be launched after that (it runs once right after driver installation, but not after the next computer shutdown or restart).
I've contacted support and once there were no any obvious solutions left like clean re-installation etc. he suggested installation from another admin account. I tried it and it works just perfectly, GFE installs without any errors. Now I'm trying to find what is wrong with my main account, as I don't like the idea of using second account to simple update the one exact program.
Thanks in advance for your help and time.