Computer won't recognize my camera?

I'm trying to get pictures off my camera, but every time I hook in into my computer with the usb cord nothing happens. I even have tried taking out the memory card and putting it into the slot on my computer, but nothing's coming up. What could the problem be?
my camera is a nikon d5000

Could be a couple of things. Worst, the card is corrupted and the computer can't read it.

This is probably a dumb question but is your camera turned on when plugged into the computer?
Okay, given all of that perhaps trying a usb card reader is the answer. Most of us regulars here use and recommend readers - I've used them for years.

If that doesn't work then I'd say the card is bad and should be trashed and replaced.

Know this however, with a new card format it in the camera before using it. Then at the end of every shoot upload to the computer… Do not use the card for storage or display. After you've uploaded format the card in the camera.

If you've been using the camera and card for storage and display this is what probably caused the card to fail. It happens all the time.