You can adjust shutter speed and aperture. I don't know how to do it as I have never used this camera, but reliable sources state the camera can. Unfortunatly you can't shoot RAW foramt. This will make correcting the colors difficult at best. We should be able to clean up the blur at least though. I am not sure exactly what the crop factor of a 1/2.4" sensor is, but a 1/2.5" sensor is 5.6. So, lets call it an even 6x crop factor. You need to take the focal length of your lens (i.e. 60mm) and multiply it by 6. 6x60 = 360. If your camera doesn't tell you what your focal length is, zoomed all the way out (telephoto) your lens is at 70mm (shutter speed should be at least 1/500) At 1/3 stop incriments, selectable shutter speeds jump from 1/400 to 1/500 (skipping the magic number of 420). 1/400 may work but is technically too slow, always round up. Zoomed all the way in (wide angle) your lens is at 6mm (shutter speed should be at least 1/40). This will give you the estimated minimum shutter speed you should be able to sucessfully use without a tripod. If you zoom all the way out and back off a little bit, perhaps 1/400 or 1/ 250 would be enough. The point is by knowing you need 1/500 zoomed all the way out and 1/40 zoomed all the way in, you should be able to make and educated guess.
Of course these figures are general assumptions. If your hands are more steady than average or you brace yourself against something, perhaps you can get away with lower shutter speeds. If your hands are extra shaky you may need more shutter speed. This is where a tripod comes in. In a Utopian world, a good tripod will eliminate all camera shake and you only need enough shutter speed to creatively freeze or blur motion. We do not live in a Utopian world and wind or your shutter mechanism (mechanical movement inside the camera itself) or just a cheap tripod will still cause movement.
Practice this method and post your results, we will go from there.
A DSLR i.e. Nikon D40 should blow any point and shoot out of the water. Physics still applies though, and a crappy lens on a DSLR may outpaced by a good point and shoot camera. I do not like the D40 or D60 because of lens compatibility issues, but I'll let our local Nikonians consult you further on that matter. I am a Canon man so Nikon just isn't my realm of study. Nikon makes a good product, I would just suggest a D80 over a D40.