A new card works, huh? The existing card may be drawing too much current for some reason (or it's got some type of compatibility issue with the camera). I'd clean the contacts on it and make sure they are nice and shiny (in case it's not making a good enough electrical connection).
As for recovering your the images from it, try Photorec (free). You'll want to use a card reader. The only problem is that if the card has some type of internal short, it could potentially damage your PC. You don't normally see that type of problem, though.
If you want to try recovering the images, I'd suggest that you download and install this software for the operating system you're using (Windows, Mac, Linux). It's free. You'll see a download menu choice on the left side of the main page. Then, just click on the desired operating system to download it.
http://www.cgsecurity.org/wiki/PhotoRec
Use a card reader and select your memory card from the list of media it finds (hard drives, memory cards, etc.), and give it a place to save the photos to on your hard disk when you are asked Where to Save Recovered Files (it defaults to saving recovered files in subfolders under Photorec, where the software is installed on your hard drive, but you can change it to something else if desired).
Note that this product does not retain the original file names (but, you may not care about that), since it ignores the file allocation table entirely.
Don't worry about changing any of the other options. Just leave everything else at the defaults (Partition type, file types to recover, etc.) and it will try to recover any files that haven't been overwritten yet (and don't try to do anything like take more photos or you may overwrite some of them).
Here's a page showing you how to use this software:
http://www.cgsecurity.org/wiki/PhotoRec_Step_By_Step
After you recover your images (and make sure you can see the larger images, not just the thumbnails), I'd make sure you format the card again before using it. Here's a utility you may want to try using a card reader since your camera can't work with it yet. You'll see a download link at the bottom of the page.
http://panasonic.jp/support/global/c...formatter.html
If you can get it to work, I'd reformat it using the camera's menu choice for format before using it again. I do that every time I reuse a card (format it again using the camera's menu choice for format versus a PC). That way, the card always starts out with a fresh FAT (File Allocation Table), just the way the camera expects it, since the camera is performing the format.