As I mentioned in my original post, I've already tried the "session_commit" fix mentioned in other's posts. Like them, it did nothing for me. Cart still just reloads the page, add to cart just reloads the page.
____EDIT_____ added later_____
As a test, I retried the "session_commit" fix again, but to no avail. I have loaded the site on two different Linux servers with two different hosting companies both running PHP5. No go on either of them, with or without the "session_commit" fix.
Any other ideas? Really hoping to get this working, as I've got three other projects I need to use this on, hopefully on one of those two servers.