First off, using any on-camera popup flash is probably not going to give you a "natural" look. You'll need to either use natural light or move your flash off camera (which I don't believe your camera supports). The popup flash (I'm assuming thats what you mean with just "flash") is on the same axis as your lens and generally doesn't produce "natural" pictures (largely because our eyes don't typically see the world lit by a bright light shining from our forehead).
Your shutter speed issue sounds like an exposure issue. With a fixed amount of light, the brightness and darkness (exposure) of your pictures will be determined by three things: shutter speed, aperture, and ISO -see exposure triangle. (Mattdm points out in a comment below, that this may better be visualized as a rectangular prism. See his comment - if you can visualize that, its even more useful.)
By going below 1/30 on your P100 in whatever situation you have, your aperture isn't large enough and/or your ISO isn't high enough to compensate. You'll need to try to open your aperture larger (lower f number) or increase your ISO (this is the light sensitivity of your sensor). These should be settings on your camera.
Its difficult to go into all the exposure details here, but there are several excellent books on the subject and many, many online sites. Try Understanding Exposure for an excellent reference.