After further diagnostics, it appears that the cache is getting a blank page inserted into it. So it delivers a blank page. By using WP Fast Cache I was able to see blank pages going into the cache and errors finally showing up.
My problem is something with my Apache setup, as I'm running just on a public IP number and the AWS instance is running on a local IP, and so the plugin cannot retrieve the page to cache it.
I couldn't tell if WP Total cache is having the same problem, but I'm sure it is. So this is not a caching bug, but a server config issue, which I'll work out later.
Thanks everyone for listening.