The camera won't have much built-in memory. I have the Z750, which I think has 16MB of internal memory. This would store about 3 of my images at full-res.
I'd also suggest formatting the card (you'll lose any pictures of it). It should be the first thing you do if you get a new card. Format it when it's in the camera itself -- there's a function to do this in the setup menu somewhere.
Also, I'd suggest buying a cheap card reader. This plugs into a USB port on your computer, and you plug the card itself into it. This means you can transfer the pictures usually faster than by plugging the camera itself in, and it also means your camera doesn't need to be switched on to use it.
http://www.ebuyer.com/UK/product/75786