You mention in your original post the tip is broken off. I'm not sure if that means a corner or part of the metal contacts or something else, but one thing you could try is using another device. Run to an office supply store or a Best Buy or something and get an external SD card reader that plugs into your USB port.
The computer's SD card reader may be thrown off because of whatever physical piece broke on the SD card, but that doesn't mean ever SD card reader will be. They are fairly cheap, maybe try a couple of brands of external readers? Or another computer?
BTW, does the DVR still read the card / show the video?