I believe this is a symptom of the same problem that I was seeing in this post:
http://wordpress.org/support/topic/w3tc-disk_enhanced-page-caching-gzip-debugging?replies=1
The blank screen appears for users that are not logged in. To further confirm, in chrome, you can go to developer view, network/headers and confirm that the "Accept-encoding: gzip, deflate, sdch" is present in the request header, and the response header is something like:
HTTP/1.1 200 OK
Server: nginx
Date: Wed, 19 Jun 2013 20:44:21 GMT
Content-Type: text/html
Transfer-Encoding: chunked
Connection: keep-alive
X-Powered-By: PHP/5.3.25
Vary:
Content-Encoding: gzip