Indeed all good suggestions. I don't know that this is resolvable with a P&S camera.
The problem is one of exposure as stated above. How do you expose for both a dark shadow (with detail) and a bright highlight (with detail)?
First - if you can - use flash, though this is not without its own exposure problems. If you can expose for the white, then use flash as "fill", you could get detail out of the shadows, but of course the risk is then over-exposing the white. The trick is to keep the flash very low power if you can, which most P&S cameras can't do.
What I do is use my in-camera multi-spot metering system, which again, a P&S or even 20D won't do.
Without fancy tricks, you want to expose somewhere between the light and dark areas. If you can average the exposure between the extremes, you'll get a good shot. That's easier said than done, but Largo, as usual, is spot on (excuse the pun)...
The key is in how cameras expose light. Cameras think that a "perfect" exposure is one where the entire scene can be averaged to what is called "18% grey".
Imagine a simple picture - 1/2 is white, 1/2 is black. The average of these colors is grey (close enough for this paragraph). Let's call that 50% grey.
Now let's imagine a scene where 3/4 of the image is white and 1/4 is black. The average "greyness" of the image has changed. It's now "brighter" so the camera will adjust itslf thinking that there's too much light to make everything even.
Now the reverse - 3/4 black and 1/4 white. The camera things the average is now 75% grey because there's more dark than light.
The camera, will try to expose all three so that they would appear to be the same shade of grey if they were averaged into one color (grey for those who haven't had their coffee yet).
Largo's suggestion basically tells the camera "I know you think this is mostly black, but let's kick it up a notch or two because I'm smarter than you", and that's exactly what happens.
If you have the ability to shoot RAW, a lot of these things can be resolved by altering the exposure after the shot.
GAD