The 'from' part which is missing in your case comes from Joomla configuration: $from = $config->get('mailfrom');
I cannot imagine that your configuration does not have set the email

Are you able to debug code? It would be interesting to know the value of the from variable, e.g. in file:
administrator/components/com_phocacart/libraries/phocacart/email/email.php on line cca 102, add some debug info:
e.g. var_dump($from);
to see what is the value of this variable.
Jan