Experiment with bouncing your built-in flash. Go to your living room and try to replicate the lighting of where you would normally be shooting. Get a business card and put it in front of your flash and bounce to the ceiling. Yes, it will make your already anemic flash even weaker, but it shouldn't wash everything out.
I had the 35mm 1.8 for a while and loved it. I fully intend on getting another. I would LOVE to have a sigma 20mm 1.8, but thats $$$.
Check out slickdeals.net if you aren't in a hurry, I've seen the 35mm 1.8 as low as $150 shipped after some deals.
Zoom in to the max zoom on your lens. Will that zoom setting be usable? If so, get the 50mm 1.8 and manually focus it. I bought a previous version of it that has some slight dust inside it for $60 used from
adorama, you may be able to find something similar. The dust isn't much of a nuisance on most shots.
The 1.8 is going to be a full 2 stops faster than your kit lens at the 18mm end, 3 stops faster than the zoom end. Also, larger aperature will help your flash seem more powerful, particularly helpful if you try the bounce trick with a business card. I would think with ISO 800, a 1.8 lens, and bouncing your flash you should get acceptable results.
Waiting for a call from work I got bored enough to find out:
1st picture, iso 800, f/1.8, 1/15 second shutter speed. I turned my lights way down, it was pretty darn dark in here. BTW: The noise on my D200 is going to be worse than the noise on your D40 at a given ISO. At full sized these looked like crap.
Then, same scene, direct flash. Keep in mind, everything was dark, nothing was terribly close to the camera (I was about 15-20 feet from the couch), nothing was light colored to get washed out.
Now, the bounced flash. It shows that you can still light up the area fairly well. Unfortunately, it doesn't show preventing washout since I wasn't close to anything light colored.