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.
Make sure that you followed the upgrade instructions from here http://doc.silverstripe.org/doku.php?id=upgrading&s=upgrade (as appropriate for your build)
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.