The site is not valid. The 'Pages' document library is missing.
ULS Log tells me that:
The site is not valid. The 'Pages' document library is missing. ......
Solution to this problem was really simple.
I've found a blogentry on blogs.technet.com, which tells me to update the "PAGES ID", and it worked well.
$web = get-spweb "http://site-collection/path-to-affected-site"
$correctId = $web.Lists["Pages"].ID
$web.AllProperties["__PagesListId"] = $correctId.ToString()
$web.AllProperties["__PublishingFeatureActivated"] = "True"