I agree with Scott.
Low light photography is a very hard subject to achieve with most digitals (minus DSLRs). Light is the essence of photography so anytime you reduce the amount of light your going to run into problems and you'll need work arounds.
What really kills you is the ISO ratings (film speed). Going back to those good old film days you might recall using ISO400 film was the ideal indoor film in that it allowed light to react quicker to the film, hence faster film. The downside to the faster film was grainy photos, a pleasant effect when shooting black and white but in color photos its not a welcome side effect. This phenomena carries over to the digital world but in most cases ISO400 with the small sensors of the point and shoot and even pro-sumer cameras its worse than film.
There are a couple newer cameras that have better noise performance at higher ISOs like the Fuji F10/F11 or the Sony H1.
To reduce the ISO noise you will need to shoot at a slower speed like ISO 50/100 this also means that your shutter will need to open for a much longer period of time and you will need a tripod. Image stabilization which is offered on the Sony H1, Canon S1/S2, Panosonics and a limited number of other cameras will provide you with some assistance against camear shake but it has its limitations.
Another aspect of digitals that are vexed by low light is auto focus. Non-DSLRs use a different type of autofocus which is not as reliable in low light. In some cases your camera will "hunt" to focus, meaning it will try and retry to find something to focus on. Work arounds for this is to use a Center Weighted Auto-focus setting vs other modes and or focus on a object with good contrast. Of course you can use manual focus as well.
I dont want to scare you away from digital photography its lots of fun. The thing to keep in mind is there is no perfect camera. You might find one camera has better performance in one aspect but falls short in another.
My personal preference is Canon. I'm currently shooting with a Canon A95 but I'm planning on replacing it with the new Canon A620. Its at the larger pocket-able size camera, it has a swivel LCD, 4X optical zoom (digital zoom is useless), 7MP and its has some other enhancements to the A95.
There is also a A610 which is a 5MP version of the camera which is more than enough for standard size to 8x10 prints.
The A620 runs about $340-$400.
As always the best digital photography site on the web is
www.dpreview.com
My A95 photos can be seen at
www.pbase.com/eddyb/a95 I'd expect the same results from the A610/620.
Ed