I agree. That answer from your host is nonsense. They *can* give you the info. But maybe their server setup makes it inconvenient to do so. As Website Rob said, hosters using contemporary systems can easily give you self-serve access to the server errorlog data related directly to your account activity, specifically on a shared server.
As to troubleshooting, you mentioned that you turned on Strict Error Reporting. Try turning that off, and use the debug error log utility mentioned in step 2a, as suggested before. That might give better clues as to the cause, because sometimes dumping error information to the screen can report symptoms prematurely and thus suppress the real error situation.
But I think your server's apache errorlog data is going to be the most useful.
If your host won't give you access to the errorlog, then get them to tell you why *their* server is blocking *your* site from functioning. (They'll have to look it up the errorlogs to find out.)



