You should check the webserver (e.g. Apache, nginx) logs for the cause of the 500 error, and will most likely also find the cause of the "half page"-dashboard-error there.
The webserver logs are different from Magento's own logs in
var/log and you should ask your hosting provider where to find them.
Also, please specify your Magento version. In 1.x, you can enable the Developer Mode either in the webserver configuration or in the
index.php file. In Magento 2.x, you can enable this mode with calling this in the Magento root directory:
bin/magento deploy:mode:set developer
You shouldn't enable this in the live-system, though, as this will lead to more errors and error messages being shown. Also, in Magento 1.x, theres the file
errors/local.xml.sample, if it is a fresh install) where you can define to have a mail sent with the full error message and stacktrace if anything goes wrong.
All paths are from the Magento root directory.