The 4300...
.... is a pretty good pocket digicam design. I like the fact it has the mid sized image sensor at 1/1.8" versus 1/2.7" sensors which are generally have more of a challenge being the smallest and having some of the smallest pixel sensor sites.
Your probable solution is to select MANUAL mode. This allows you access to shifting/setting many aspects of the camera while still enjoying automatic exposures.
Go to the "SHOOTING MENU" and select "ISO". You will have 3 choices... 100, 200 and 400. Your grainy images are most likely from the camera selecting 400 automaticly. For the BEST quality... you want to take it off "AUTO" here and reset it for ISO 100. If the light is somewhat dim - you can go into the menu and reset for 200. Using 400 is probably the point where your image sensor produces images that are breaking up... otherwise they would have given you an ISO 600 or 800 setting. I suspect that even ISO 200 has noticable noise.
There also is an option to activate "NOISE REDUCTION". Once enabled it acts when your shutter speed falls below 1/30th of a second. Obviously, at this speed you need a very steady hand or tripod. You know - as inconvenient as it sounds - making use of a little pocket mini-tripod (legs about 2-4" long) can improve you shots in dim light tremendously.
Here is what one review on your camera said about the manual mode. It is not critical at all - just explanitory about what the "M" mode does:
Manual Mode: Following Scene mode, Manual mode (black camera icon with a "M") gives the user control over all exposure settings, with a choice between Manual and Program AE exposure modes (accessed through the Shooting menu). (Note that "Manual" mode here means that you have control over multiple camera functions, although shutter speed and aperture remain under camera control by default. The "full manual" mode I've referred to above is accessed via a menu choice from within this mode (see below) and lets the user control shutter speed and aperture directly.) The Shooting Menu offers the following options:
I might add that if the lighting gets a little dim... you MUST take very steady shots. Lean against something that is firm or SOLID... like a wall. Also, when the lighting is dim your subject must also remain still. HOWEVER, if the lighting is really dim and the subject is CLOSE - your camera should trigger a flash automaticly and your image will be captured if close. The lighting will probably appear artifical with a flash but - often a flash can stop the movement in your subject like a brick wall to a flying egg. IE, jumping into a pool the flash will create a frozen moment with the water spraying about ... that is ... if your AF can get the focus right. Your flash range is about 10 feet or 3M. The various sites give different values and interpretations of this - so just assume its a 10' range.
THE FINAL consideration.... you should make certain your image capture setting is at "Hi-Quality" (only available in 2272x1704) or "Fine Quality". You have two lower quality capture settings - "normal" and "basic". I can easily predict that if you were shooting in "basic" and low light with the green "A" AUTO setting - then your images are certain to be grainy looking. However, your memory card will give you the most number of shots. Setting your camera to the "Hi-Quality" setting will drop your shooting capacity to its' lowest. If you can't take enough pictures with your best (largest) card... then go buy a single huge memory card - memory is very cheap now! Shoot in the highest quality your camera is capable of (you paid for that power!)... and steady your shots in ISO 100. Try using a minipod and remember the few shots where you used the pod when reviewing the finished shots. As long as your subject is not also moving - your images will be of the best quality that your camera design can produce.
Hope this helps.
Tomorrow I'm gonna visit North America's largest Anime convention! 100s if not 1000s of people will come out in full costume dressed as their favorite Anime characters. It should make for a fun photo shooting opportunity. I've never been to one of these before and it is sure to be "colorful" if nothing less! Here is an image of what I'm expecting:
I referred to DPreview, DCResource and Imaging-Resource to patch together this reply. Take a look at these sites for insights into the capabilities of your camera.