Thanks for replies. Jut for info OS is Win XP. And exe names in game folder have no "eu" in them.
For some reason, when I run the updater in that game folder,"cohupdater.exe", no checksum happens. But when I run the first file which was downloaded from the site on my desktop, "cohupdater.eu.exe", it did verify and now game runs. I also deleted "coh checksum" file, dunno if it helped this "eu" file but the other update exe in game folder definitely doesnt verify. You also need to select the folder your "City of Heroes" folder is in.
So basically if you encounter this problem, use the downloader/updater you got from site, not the one in game folder.