How close should the lights be to the subject?

If you are actually using the lights you linked to, something is not right, here. That's plenty of horsepower.

How are you triggering the strobes? How are you setting the exposure on the camera?

Separately from those issues, though... get your subject a little farther away from the backdrop, and yes, move the softboxes closer. Even a couple of feet will meka huge difference in the quality of the light. But mostly: set exposure manually, using a low ISO, perhaps 1/125th on the shutter, and around f/8 on the lens. Then adjust the lights to get yourself in the neighborhood, power-wise.

I'm guessing you had to use the on-board to trigger the flashes? If so, turn the on-board down to minimum power (set it manually and select 1/128th or whatever the minimum is). Not TTL.

In addition, you could completely eliminate the effect of the on-board flash by blocking the visible portion of the spectrum with a $12 SG-3IR or similar infrared filter.

I don't know nikon as well as canon, but if you are using the on board (popup) to trigger the strobes with a canon, then you will not see their effect because the TTL metering fires a short preflash which will fire your strobes before you take the picture, leaving them drained when your TTL popup flash actually fires the main flash.

Do you have a sync cord?

If you do, consider keeping your on board flash off and only syncing to the one strobe... then you should get "strobe only" lighting.

Maybe someone can step in an tell us if the Nikon on board will ever fire in manual mode.. the canon you are stuck with TTL unless you go with a speedlite.

I had exposure set to automatic, which may be my issue. The strobes are constant, are not triggered by flash. I just felt like I had to use the on camera flash to help brighten the picture.

I apologize, I put the wrong light kit in the link - it is this one:

HERE

Th one above has a ton more wattage than mine currently does. Is it possible to replace the bulbs that originally came with the unit with stronger ones? Will it damage the lighting units if I do that?

Oh, alright then, you're just going to be shooting using the ambient light..

I don't know much (anything) about constant lights (AKA hot lights, even if these are "cool")
For better results strobes will provide much higher f/stop (f/8+) and your max sync speed... have you looked into alien bees? I just picked up an AB800 and am pleased with the results.

If you can return the kit and purchase a Nikon Speedlite you will be much better off for what I think you are trying to do... and Nikon has commander mode which (I think) allows you to use TTL with your off camera flash (but I prefer manual flash exposure in this kind of environment where it will be more consistant)

You are currently using lights -- not strobes (flash). And the lights that you are using aren't powerful lights. In many cases, the brighter continuous light setups use tungsten bulbs instead of the fluorescent bulbs that you are using. Tungsten is usually brighter, but they are hot hot hot. I suppose that you could try to move the lights in very close to the subject (2ft. max), as that might help. But you will still have a problem with getting decent shutter speeds and decent depth of field. Also, with the lights up that close, you may encounter problems with the depth of light (that is, the light falloff behind the subject will be very dramatic) that will be annoying in situations in which you don't separately light the background. I think that you should get strobes.

Hi, I would definitely move your subject away from the backdrop, at least 3 - 5 feet. Otherwise shadows end up behind like hard dark halos. I made this mistake once with film and I spent a lot of time dodging afterward. When I noticed that, I thought I had to say something along the lines of "avoid my mistake!".

From a strictly physics point of view, intensity of light falls off as 1/(r^2). That is, one over r squared, where r is distance. In this case, the distance between the light and the subject. That means if you were six feet away, and you are now 3 feet away, you have four times as much light as before (intensity was 1/36, but became 1/9 when you moved).

There is no one answer to how close the lights should be, it depends entirely on the effect you want to achieve. The closer you move the softboxes to your subject the softer the shadows will be because the light source will be relatively larger and seemingly coming from a spread of directions. By moving the lights further away the shadows become sharper. By moving the background further back the background will be darker as suggested above because of the light fall-off. Even a white wall can be made to look black with sufficient light fall-off. You may wish to make the two lights have different intensities to make one the key or main light and have the other at less intensity/greater distance to provide some light in the shadows cast by the key light.
You are at the beginning of a journey on lighting. For an excellent guide on that journey go to Strobist.com