I've got a client who has a very odd problem that appeared out of virtually nowhere. It seems that their site is caching absolutely everything that could possibly be cached. I've turned Magento cache off and talked to the hosting company, and there is apparently no caching set up for the site right now.
Right now, if you place an item in your cart for the first time, everything seems to work fine. If you attempt to remove an object, the cart will appear to still have the item in it. The only way to get the cart to update is to refresh the browser 2 or 3 times. If you attempt to put another item into the cart, you must refresh the browser to get it to appear in the cart.
If you log into the admin panel and try to clear cache, reindex, turn on path hints, or really do anything that would show that you updated anything on the back end, you have to refresh the browser to get it to show up. So, for instance, say you tell the site to reindex the search engine. The site will act like it's reindexing, then do the usual auto-refresh, but the search engine will still appear to need indexing (ie it will be red) until you hit F5 to reload. Then the search engine index warning will turn green.
I'm at a loss at this point for why the entire site is caching like this. I have a dev site that is roughly identical to this live site and it's not having any of these problems. The only difference is that the dev site is hosted with a different company entirely.
The only StackExchange post I've seen that resembles this issue is here, but the reported fix didn't work for me. Any help is much appreciated.