Error 500 only on permissions page
Because you are on shared hosting the PHP process may not be given enough memory.  If you have a complex site or page the drupal bootstap may run out of memory and fail. I have had this problem trying to run a heavy site (one of the more Drupal complex distributions) on a shared host.  I would take a quick peak at how much memory is given to a PHP process (and Drupal) by visiting admin/reports/status and look for the "PHP Memory Limit".  I typically use 128M on a complex site.

You said also you can't edit you php.ini file - are you certain?  Many shared hosts allow you to to override the global php.ini file with one in your account.  Most will have a wiki explaining how configure such overrides.  If not you may need to move to a different host.