Enable "error logging to file" in your php.ini (if supported by your host). This should help track down issues occurring before the internal debug logging in Zen Cart is loaded.
You will also need to edit the section pertaining to STRICT_ERROR_REPORTING in the Zen Cart admin (/admin/includes/application_top.php)... Either set it to true (or if you have edited the php.ini comment out "error_reporting(0);")... Just don't forget to reset the file when done with testing...
Usual causes are: files uploaded to wrong locations, files "backed up" via file copy (and left on the server), and mistakes doing any manual merging (or caused by previous manual merges to any of the "modified" files).
NOTE: "Plugin Manager (full)" usually handles issues during an upgrade better (and will usually result in a Zen Cart debug log if an error occurs) as an init_script is not used. If you have access I would recommend using this method instead... One can always uninstall "Plugin Manager (full)" afterwards.