EASYSHARE Z1012 IS Digital Camera: Noise Problem  

So I recently got a replacement camera for my Sony DSC-H2. Because of the way sony was towards my old camera I decided not to go with them again. Their cameras while amazing have a huge flaw and that's the shutter button design. It's not housed in the casing rather just spring loaded. I had mine for a year and a half before it just popped right off without any warning. Needless to say I was a bit teed off especially with it being around Christmas. I finally took it to the store that I bought it and they found no physical damage and were perplexed just as I was at the design of the camera. Any ways they bought me out and I decided to go with the Kodak EASYSHARE Z1012 IS Digital Camera. HD video many other options I didn't get with my other camera and great pixalage. however I started taking photos and noticed one major problem.

Noise NOISE NOISE! I figured it was something to do with the settings to I changed them around. Still nothing. I tried different kinds of lighting. The only time the noise wasn't there was when a flash was used in close proximity to the object.

My question is if anyone else has had this problem with the camera or if there's anything that can be done to fix it that I just haven't thought about.

I got a Nikon D90 but I'd like to be able to use the Kodak in a pinch or when I just don't want to lug the big camera around.