Digital camera wont download pics to com...

I have an olympus stylus digital camera and when I insert the memory card into the computer, often times many of the pictures won't show up. The number of the picture shows up but the computer won't let me view it. Then when I insert the card back into my camera it will say that I need to clean the dust off with a dry cloth. I do that but the camera still keeps saying that or giving me the option of formatting the card. Obviously if I format I lose all my pictures. When I try putting the card back into the computer it tells me I need to format the card. This has happened several times and I've ended up re-formatting the card and losing all my pictures. This time I've got important pics I really don't want to lose. What should I do? Is this a problem with the camera, the card or my computer?