It turns out the problem was a configuration server problem. The admin turned off Open_basedir and all of my headaches, at least on this front, are gone now.
I am not sure what open_basedir does exactly, but I think it was originally pointing to a folder outside wordpress, so the Ajax calls in the dashboard were affected by it, which would generate an incorrect path to the Ajax file to load, admin-ajax.php, preventing it from loading.
Answer pulled from OP.