No such file error so the first thing to check is to make sure sapphire/core/Core.php exists and is readable by the webserver user. Hmm I wonder if it makes a difference that its core/Core where as on Windows it might need to be core\Core I would be surprised if that was the issue.
It sounds like something went really askew with your upgrade process. The path sapphire/core is a major part of the silverstripe framework, and is something that will have been there in the original installation as well as the upgrade.
I struck the same problem installing Silverstripe on Win XP SP 3, XAMPP. The problem with the missing /core files was with the extractor I used. I used Winace to extract the files initially, and the /core files were missing. Then I tried using 7-zip ( http://www.7-zip.org/ ), and it extracted all files accurately.