Suspect you won't get much with a D3000. Simple test, get an IR remote control (TV generally is fine - make sure you can't see anything yourself when you press the buttons and you're good to go). Point at camera, take a picture with sufficient exposure to make sure you've caught the button press. If you see an image of a bright light the camera is able to see some infrared light. If you see a dim point it's mostly a waste of time. (All this is easier if you have a camera with a live view mode!)
I don't have a Nikon, but from what I can see on the web I expect you'll see a faint spot. My Canons are like this, and would be pretty useless, my Panny LX3 can see a nice bright light and can take (slowly) IR images, though it shows a serious degree of flaring.