Seems like a strange problem. You could format the card in the camera which should erase it.
If I were you I'd try looking at the contents on a computer then formatting it in the computer then put it in the camera and format it there again. The formatting you did may have put some eroneous data on the card.
Your computer might have an SD card reader slot or you will need to get a USB SD card reader
Assuming you can read the card via the card slot on your computer or a card reader the card will show up under "This PC" or "My Computer" depending on your OS. If it is and Apple computer then I dont know but it should show up as a drive
On a windows PC when you find the SD card it might say Canon DCIM right click on it then look down the list for "Format" click on that to format it
Shooting video requires very fast high speed SD cards. Make sure the card you are using is at least a Class 10 card. Also be sure it's SDHC or SDXC and not just SD.
Try a lower resolution video to see if the camera works with that mode. (Ie. VGA vs HD). Does the card allow you to take still photos? If not, then there could be an incompatibility of the SD card with the camera. I would try a different brand SD card just to be sure.