Computer can't recognize SD card?

I have a coolplix digital camera by Nikon, which is a few years old. I just got a new Gateway computer with a digital card reader slot that can be used for xd/SD/MS/ and MS pro. However, this will not load the SD card on my Windows 7 Home Premium computer. It is a San Disk SD card 512 MB. What is wrong? I mean the computer won't make any noise or nothing pop ups on my screen when I put the SD card in the reader slot. I never had one on my old computer so I don't know much about them. I checked to make sure my SD card was in the unlock position and it was, and there are still photos. I just need some advice on how to get my computer to even recognize it. Do I need any updated drivers for it. All my USB ports work, is there a separate driver needed just for digital media like SD card readers. Help please. Thanks.

Added (1). Where in Device Manager do I find the memory card reader, what is that under

Added (2). I don't hear a clicking noise.

The card reader should recognize the SD card right away. In some machines you should put the SD card on the slot and press it firmly until you hear a click and the card locks inside it. To remove the card you press it again to unlock it.

You may have to install a driver for your card reader, go into your device manager, and make sure everything is installed properly. Also, try going into My Computer, and checking to see if there are any removable devices there that you don't know about.
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In Device manger, it should show media readers, or something like that, if not than visit the website of your Gateway, enter the model number, and find the driver for your media reader.