Point and Shoot cameras are notoriously noisy at high ISO settings to the point that they are practically unusable. This is especially true of my own Canon SD800IS.
Recently I discovered DFine 2.0 and decided to put it to the test. The photo here was taken in my kitchen at ISO 1600 with no flash. The left side of the photo is unprocessed. The right side has been run through DFine 2.0 in Photoshop. I used all the default settings and did no other processing in Photoshop. Even with minimal work I think the result is quite good.
At $100 DFine is pretty expensive but it does a good job at rescuing such photographs.