Hi, Just to give some light
The new WP release 3.9.2 has a important change related to the login area, cookies and hashes, this will broken any plugin that uses the old integration.
For what I see the error 500 is caused by a combination of plugins that try to use part of the login area in a loop or by internal http fopen file_get_contents etc without a good error handling. Try disabling any plugin or enhancement related to the login area, with the important plugins activated
ACF
Contact Form 7
Woocommerce
WP Bakery