It's very difficult to pinpoint an issue with what you've given here. Particularly since flash photography at night can be hit or miss anyway.
I actually wrote a review for Popular Photography & Imaging on your camera... You can read it here:
And while I really LIKE your camera, it does have its' limitations, particularly with the flash at night. It's small and not very powerful in comparison to a full-size/feature flash unit. Because of this, here's a few things you should keep in mind when you shoot at night with a flash:
Allow the flash enough time to "recycle". In other words, when the flash fires, it needs to replenish power to make another full-power flash exposure. If you're shooting images very quickly, you may not be at full power for each frame. The T10 has a flash-ready indicator, so make sure it's activated before you shoot your images.
Stay close- There's a thing in photography called the "Law of Inverse Square". Basically, this means that when you double your flash-to-subject distance, your light intensity is cut down to ONE QUARTER of your previous distance. The T10 has a very small flash, so this becomes critical for good images.
Be reasonable in your expectations. The T10- or any other camera-mounted flash for that matter, won't light an entire stadium or something that's more than 10 feet with your flash or 50 feet with a full-power/size flash.
If you're following these guidelines, and you're still having issues with dark images, try upping your ISO to a higher setting to add some sensitivity to the sensor. Doubling your ISO cuts the light required to make a good exposure in half. If you've done this and the images are still black, you may want to take the camera to a repair shop for evaluation.
I shot several photos that should be included with the story on POP's web site, so you can see that the camera IS capible of shooting some nice flash image, but again, were done with an understanding of the camera's limitations.
Hope this helps you out!