Elements are two different programs. Is your copy of CS6 still working? You should be able to open any files created in Elements with Photoshop CS6.
Are you trying to open files when you get that message? Then it's probably the file associations. The app/version installed last will take over all file associations. So if you installed an Elements trial after CS6 that's how it would behave.
An added complication is that if you uninstall "out of order" the file associations often get messed up. Try first to set the correct associations in the OS, or Bridge if you have that. If that doesn't work (it doesn't always) a reinstall should fix it.
It's a bizarre thing. I have CS6. It was purchased by my IT dept. a year ago. About a month or so ago I started getting the message that my "Elements Trial will expire in 30 days.". I thought it was a mistake, but apparently not.
Coincidentally, this seemed to occur at around the time that my company implemented a backup software, so I'm wondering if it had something to do with that.