Sometimes, in some browsers, my website incompletely renders

I posted this in a main WordPress forum. It was suggested I repost it here, as I’m using Graphene.
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I manage two different WordPress web sites. One of them is giving me no rendering problems at all. (That one doesn’t use Graphene.)

The other, which uses Graphene, is giving me very inconsistent rendering:

1) It seems to render consistently in Opera, SeaMonkey, Safari, and Internet Explorer, as I go from page to page

2) However, when I try to use Google Chrome or Mozilla Firefox (my first and second favorite browsers), I get very inconsistent results. Sometimes, I get a completely blank rendering; sometimes, I get just the background image and nothing else. Sometimes, I get the main page rendering, but when I try to go from page to page, I get the incomplete rendering again.

I’ve tried clearing the browser cache, and this seemed to fix the problem, but then it comes back.

I’ve also tried to clear the WP Super Cache on the web site, and turn it off and back on again.

This seems very mysterious, and I’m wondering if you have any insights on what might cause this, and what I can do to figure it out.

I appreciate any help/advice I can get. Thanks!

FWIW, I’m running WordPress 4.2.2, using the Graphene theme. If you want to look at the web site, it’s at http://souheganvalleychorus.org/