Need a camera for indoor dancing with mid to low light

[Rommel]

So I am looking for a sub-$400 camera to take pictures of my girlfriend who competes in ballroom dancing competitions. They take place in large ballrooms with usually just the dance floors lit and I need to take them at distances between 10 to 40 feet (I am not allowed on the dance floor). We have a 4MP older Fuji now and with the flash on its just not strong enough to get a good picture and with the flash off the pictures are always horribly blurry. Therefore I guess I need something with higher ISO settings, image stablization, and the likes. Optical zoom of at least 3x, good image quality (wont be printing large pictures), and burst modes are preferred.

It also needs to be something in the small P&S size market, not looking for an SLR although I know that would be ideal for this type of shooting. I was looking at the Fuji F30, Canon SD800, and the Sony DSC-TX series but am open to anything that will provide the best pictures for this type of shooting.

Any help appreciated!

-Rommel

[griptape]

We have a 4MP older Fuji now and with the flash on its just not strong enough to get a good picture and with the flash off the pictures are always horribly blurry.
With the flash off, assuming you're not setting the shutter speed yourself, the picture is blurry because the camera has to have a longer shutter time to let in enough light. And you're simply not going to find a very powerful flash in a point and shoot camera. If you're not willing to go the DSLR route, you might actually be better trying a remotely triggered slave flash (it flashes when it sees your camera flash).

[tim11]

Flash won't have the reach and if it's not practical to set up remote flash like Griptape's suggestion, the only solution left is finding a camera that performs best without flash.
F30 best fits the bill with it ISO to 3200 and IQ is relatively clean compared to others. However, its burst speed is very slow.