Hi,
first check this:
http://www.prestashop.com/blog/en/the-500-internal-server-error-explained-solved/
Then if you issue is:
Parse error: syntax error, unexpected T_PAAMAYIM_NEKUDOTAYIM in /home/..../classes/controller/AdminController.php on line 3101
Try this solution:
http://www.prestashop.com/forums/topic/338268-1-click-upgrade-from-1606-to-1607-admin-screen-not-shown/
It worked for me.