Look in the Magento bootstrap file (index.php), you’ll see lines similar to the following:
#Mage::setIsDeveloperMode(true);
#ini_set('display_errors', 1);
Uncomment these. In a production system, you’d never want to have your errors display to the browser, but while developing having an errors and warnings thrown immediately in your face is invaluable. This way, you will see the actually problem which lead to the Internal Error Server. In almost cases, the reason is that there is an exception throw after output is sent to browser.
Solution #1
This error might be caused because you have not set the correct permissions for the magento folders. To solve this go to File Manager and then change the file permission of index.php file from 664 to 644.
Solution #2
If you are getting weird 500 internal server errors on specific pages of your site, it might be a matter of resources. I was getting internal server erros on some product pages and on the http://yourdomain.com/checkout/onepage. I found out that the .htacess file of my magento installation was somehow reset and the php_value memory_limit value was set to 32M as soon as I raised it, the internal server errors vanished! You should use at least 256M for over 600-700 SKUs. Magento is very resource hungry and it is easy to get these kind of errors if you try to save some bucks from the hosting.
Solution #3
Htaccess file which is located at Magento root folder. It will be this case if you meet Internal Server Error on every page. Try to remove it for testing purpose.
If your website was running file for a long time, then it must be a change at Server side, just submit a ticket to Hosting Company.