I didn't say that I do not have access to log, I only said "no logs helping to find the issue". Log only show something like this:
[05-Sep-2014 22:29:18 UTC] PHP Fatal error: Out of memory (allocated 36175872) (tried to allocate 786432 bytes) in /home/area101/public_html/wp-content/plugins/wordfence/lib/wfBrowscapCache.php on line 4100
However, notice that the above log concerns problems on previous dates.
If I do what you ask ("activate the plugin, try to access the parts of the theme you need to, and then deactivate the plugin") no errors are shown.
My theme is PageLines Framework 2.4.5 (the same for working and not working websites)
Bye,
Christian