When we enable the wp Super Cache plugin, WordPress quits using 301 redirects when you try to access a site without typing the trailing slash. For example, "wordpress.org/support/" would work just fine but "wordpress.org/support" loads a blank white page. This is odd because one would think that if it wasn't going to redirect, it would get a 404 error, but instead it just loads a blank page.
We have a testing subdomain for our website, and when we enable the plugin on the testing site, everything works fine. Since they have identical .htcaccess files, I don't think that is the problem.
We also noticed that the cache status message (from the debug tab of the admin panel) doesn't show up whether you include the trailing slash or not, if that helps you determine the problem (it DOES show up on the testing site, where everything works as expected).
Hope you can help us figure out the problem!