Can I shoot in the dark with my DSLR?

I have a Nikon D7000 and i'm an amateur/enthusiast photographer. It is my first DSLR, so i'm relatively new to photography. I usually shoot on Aperture priority or shutter priority. I was just shooting around my house the other day playing around with the settings, and i turned off the lights in my livingroom so it was completely dark. The only lights in the room were from the led display on the cablebox showing the time. I tried taking shots with the iso at 6400. The problem was that it didn't want to take the photos. I then tried focusing on the time that was on the cablebox and it took the shot. I then tried it with the built in flash and agian it didn't want to take a photo. Before i had the D7000 i had a canon point and shoot. It would take photos with the flash in completely darkness without any problems.
I'm not sure if i'm doing something wrong, or if maybe DSLR's can't shoot in complete darkness. I'm not saying i need to shoot in complete darkness, cause i don't. But is it possible.

PS. I was using a kit 18-105mm f/3.5-5.6

Since photography depends upon light to illuminate the subject, what do you think?

What other than light would produce an image?

If you are using a flash, it will illuminate the subject with a preflash to help the lens focus and then the actual flash to expose your subject

Yes… However.
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Try M…
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Some cameras have a auto focus assist light. Either a IR beam or a visible beam of light so AF can be done and then the D (distance) can be set by the camera.AF-D.
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The 7000 has a auto-focus assist light. However, on M, you have to do it yourself and you CAN make the camera go off.
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By using time exposure, B… You can take images in 'darkness' where the human eye can't see in, but still acquire images. Most is trial and error, and bracketing.
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Take your camera OFF anything "auto". Aperture priority or shutter priority and try shooting on pure Manuel for a while. I bet you will discover a WHOLE lot more of what the camera can do, and get better pics.
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Totally! Simply use the aperture priority setting. It most likely has a capital "A". This will keep the shutter open longer, letting in more light, making for a lighted up photo in the dark. However, if you do this, you MUST have a tripod, or everything will come out blurry.

The flash on a DSLR will not pop up automatically unless you are set on the fully automatic "green camera" icon.

You are probably set on AF-S, which requires focus confirmation before the shutter will release. (That's the default setting anyway.) Switch to AF-C (continuous) and the camrea will work even without focus confirmation. You can also use manual focus and it will work.

If you want to actually focus on something, you can turn on the auto-focus assist light. You'll find that in your menus somewhere.

I have a D300 and the D7000 should be able to do even better in darkness.

Here are a few samples taken in near darkness.
ISO 3200:
ISO 6400:
ISO 6400:
Some ISO 6400 samples