Black screen, put in new battery no change!???

For both of your cameras, this sounds like it might 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 the following two links for more info:
http://camerarepair.blogspot.com/2007/11/canon-digital-cameras-showing-black.html

http://www.usa.canon.com/consumer/controller?act=PgComSmModDisplayAct&fcategoryid=225&modelid=13390&keycode=2112&id=29819

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 200a/300a/400/450/500

I highly recommend that you follow up on this, especially for the SD110. I think you'll be very satisfied with Canon's excellent customer service!