Things to check first are battery contact points, and micro switches that are located on the battery and memory card doors. Details on what needs to be checked
may be seen here. It won't work for every case, but it's worth a try.
But if the camera is powering on, but giving you a black screen, this would be a defective CCD imager. If so, Canon should fix this for you for free, including free shipping both ways. This is regardless of your camera's warranty status.
Please check this link for more info.
Applicable cameras include:
A40, A60, A70, A75, A80, A85, A95, A300, A310, S1 IS, S60, S200, S230, S330, S400, S410, S500, SD100, SD110, IXUS V2/300/400/430/500, IXY Digital 30/30a/200a/300a/D320/400/ 450/500