Yes, it will remove some functionality temporarily but that would help speed up the troubleshooting process.
Anyway, the Google Publisher plugin is throwing an error and there's also a 500 Internal Sever Error with admin-ajax. One possible cause of that is third party plugin conflict.
We also need that you completely remove W3 Total Cache for troubleshooting purposes. It is possible that it is causing this issue. You can install it back once this issue is solved.