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Interesting, usually I hear it doesn't work on WAMP ;)
I've been looking into this, but don't have any real answers yet. But I do have a couple of thoughts.
Cookies might have something to do with it. Since you have a XOOPS running on
zirafoviny.cz/ and are upgrading a system on
zirafoviny.cz/_test/ there is some chance that the cookies are interfering is some way? Try and delete the cookies for the domain, and then retry the upgrade. (In Chrome, I would suggest using incognito mode to try the upgrade, but I'm not that familiar with Opera currently.)
Also, it is possible there could be a related error message being swallowed. In upgrade/index.php on line 24 you should see:
error_reporting(0);
Try and change that as follows and retry the upgrade to see if it reveals anything relevant:
error_reporting(-1);
If neither of these reveal the issue, I'll investigate further.