Doesn't look like the camera has any built in memory. It won't work without the SD card. Camera is a Canon PowerShot S2IS.
I have the S1IS, and I had a problem with the image sensor (which was fixed super-fast and free of charge). On their website is a list of known problems. Try checking there to see if yours is listed. There is also the possibility that you have a defective card.
ETA - I Googled your problem, and the suggestion given most often is to get an image recovery program for your computer. You might be able to recover your lost photos. Also, they say not to use the card for anything else, because you might overwrite the missing files. You can begin here.
http://www.z-a-recovery.com/digital-image-recovery.htm. I haven't tried this myself, so I can't vouch for its usefulness. I just wanted to give you a place to start. I really hope you can find your photos. I know how heartbreaking it is when this happens.