I got to the final point where I call some page in my shop. I believe all the database updates were done, now the applyUpdates() method is being called, but the following error appears:
Fatal error: Call to undefined method Mage_Core_Helper_Data::useDbCompatibleMode() in /Applications/XAMPP/xamppfiles/htdocs/shop/app/code/core/Mage/Core/Model/Resource/Setup.php on line 308
The mentioned method is in the core_helper_data class, so it seems as the system doesn’t see the whole class.
Have no clue where to go from here, any help would be significant.