If you use Program (P) Mode, you can simply switch off the flash and the camera will try to work out an exposure for you.
Change the ISO on your camera to a high value such as ISO 1600 or above. Use Aperture priority and set the aperture to a fairly useful aperture such as f8 or f5.6 to allow as much light to reach the sensor as possible. Shoot in RAW mode as this will help you to recover shadow detail when editing.
High ISO will introduce noise but this can be removed by using specialist software such as the free Noiseware (See separate blog below).
Using these option should allow you to get some type of photo and then you can use editing software such as Photoshop Elements to try to improve the results.