This looks like an error specific to your system. Either custom development, weird stuff done m third party extensions, or both.
PHP provides you with all the information you need to debug your error.
If you parse apart your error message, first there's the error
Fatal error: require_once() [function.require]: Failed opening required 'DIR/composer/autoload_real.php'
As others have pointed out, the magic constant __DIR__ is being included literally in a string.
Second, in parenthesis, PHP lets you know the include paths during the request
(include_path='
/homepages/1/d372694303/htdocs/Magento 1.8/app/code/local:
/homepages/1/d372694303/htdocs/Magento 1.8/app/code/community:
/homepages/1/d372694303/htdocs/Magento 1.8/app/code/core:
/homepages/1/d372694303/htdocs/Magento 1.8/lib:.:
/usr/lib/php5')
These look pretty standard (although personally I wouldn't include a space in your "Magento 1.8" path name, but I'm old)
Third, and finally, PHP tells you where the error happened.
in /homepages/1/d372694303/htdocs/Magento 1.8/app/code/local/Elite/vendor/autoload.php on line 5
So line 5 of app/code/local/Elite/vendor/autoload.php is where the error occurred.
As to why it occurred, it looks like someone is trying to use composer to install something in the Elite folder. This could be how the extension/theme provided in Elite shipped, or it could be something another developer has done to the system.
When you disable to cache in Magento, the things Magento would normally pull from cache need to be regenerated. That means more, and different, code runs. Turning cache back on won't fix this, and Magento first needs to cache something before it can pull it from cache. My best guess as to what happened is a developer was working on something in the app/code/local/Elite folder, something that normally isn't called when the system is cached.
