500 Internal server error. Is there any way to debug and get more information.

Can anyone tell me what are the best methods for debugging why error 500 was thrown for my site? I have OpenCart installed and suddenly stopped working. Now there are 500 internal server errors and I cannot access admin and frontent. I checked the htaccess files and they are ok.

Also, along with all the different folders like admin or the root website, core dump files are created. Everyone starts with the core. with numbers attached as core.1024 with a file size of about 42MB.

I contacted my hosting provider and they said the problem is with the OpenCart code, but I can't find any solution for this. Help me please?