Your C-2040z had some benefits that are hard to find in most newer models.
One is it's extremely bright (f/1.8-2.6) lens.
Most cameras have a lens that doesn't start out until around f/2.8. At f/1.8, your C-2040z was more than twice as bright at it's wide angle lens position.
That means that shutter speeds will betwice as fast for any given ISO speed in low light without a flash compared to the vast majority of compact cameras on the market now.
Since I see some existing light photos in your album, you may want to take this into consideration when shopping. You'll probably need to use a flash with most models in some indoor conditions that you got by without one using your C-2040z. Otherwise, you'll get motion blur unless you're using a tripod and your subject is stationary.
To get a better idea of how Aperture, Lighting and ISO speed impact the shutter speeds a camera will need for proper exposure, see this handy online exposure calculator. Note that Film Speed is the same thing as ISO speed: