I've been playing around with the W3TC settings after reading Ihor Vorotnov's post. My suggestion above did stop the white screen, but when I ran GT Metrix, I got a score of 70 page speed and 87 yslow (I have 2000+ pages), which are not optimum scores. And page load speed of 3.77 seconds, which is not too, too bad - I had a site once where the page load speed was 24 seconds - yikes.
So I unchecked all options in debug mode - since it says at the beginning of the section "Performance in this mode will not be optimal, use sparingly and disable when not in use." I'm not using debug mode, mainly because I wouldn't know the first thing about it and ignorance is bliss...so I unchecked them all.
GT Metrix score was now 86 page speed and 89 yslow.
Then I turned off Amazon CDN.
Score was now 96 page speed and 90 yslow. I thought a CDN was supposed to improve site's performance but my findings were not supporting that.
THEN, I turned browser cache back on (I just wanted to see if my changes somehow fixed the white screen also) and I added the 5G blacklist from this page http://perishablepress.com/5g-blacklist-2013/.
Final score is 96 page speed, 92 yslow, page load time 1.06 seconds (for 2000+ image-heavy pages, although all the above tests were just for the front page which is the most image-heavy).
I then tested it in Firefox after clearing cache and Internet Explorer which I haven't used in weeks so there should have been no browser cache, and no white screen of death. I'll check them again at the end of the week and see if my changes hold up. If I get the white screen again, then the browser cache is being turned off permanently.