The short answer is yes, you will have to get a much more expensive camera to take available light pictures indoors. If you look at the EXIF information you will probably see something on the order of ¼ second shutter speed for your indoor shots without flash. That isn't enough to handhold without inducing blur and anything moving will really blur. You could put the camera on a tripod and everything would be sharp that isn't moving.
Download the free EXIF Image Viewer and look at the shutter speeds of the blurred shots: http://home.pacbell.net/michal_k/exif_v.html