I'm trying to activate windows 10 with bought key. I get error that it can't reach critical servise of Windows system and to check internet connection. My brother friend done the installation, I didn't change hardware.
It's Windows Enterprise.

Well, if he somehow paid that price for the service, you should call them up.

If that isn't a legitimate enterprise licence copy, you're 'screwed' and should look into systems you don't need some arbitrary licence for, like many *Nix systems, or …something else, I guess.

He didn't paid for inst. I believe. But if I have both the key and Win10 software (it came with the key), which should both be legit, I just need to reinstall the genuine version and enter the key, right?

You probably need to do a *clean* installation, not a reinstall.

Well I tried that and I got various errors. Like this version of windows isn't supported by this tool, etc...

Google for and download and install "Microsoft Media Creation Tool". With it you can create an USB installation media, I believe (I've done it only for Home and Pro versions, I don't recall if it is possible for Enterprise as well).

With that installation media you can then do a clean installation, you can even delete all existing partitions so that no other Windows 10 recovery partitions will be left behind, the installation creates a new recovery partition.

I always clean-install Windows 10 this way when buying a new PC (laptop), to get rid of all preinstalled junk and shit by PC vendors.

If all else fails, you can always call the Microsoft support.

Why the hell are you using Enterprise? That's basically intended for businesses and usually licensed under a volume licensing key. Sounds shady to me, which may be the reason you can't activate it.