If the card slot is not working the fault is either the driver being missing or the card reader is damaged .. If you know it works ... just go to the support site and download the driver for it and install it ..
If the card reader was not a standard on this desktop , there is a possibility the driver is not on the hp site.. and you have to see what model is the card reader and what make and go to their support site ... (the card reader's manufacturer site )http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?os=228&lc=en&cc=us&dlc=en&sw_lang=&product=3254035#N152
If it seams that it has no driver fr the card reader i suggest to install the driver for the chip set .. maybe the card reader is not see cause it does not have all drivers for buses..
another way to install teh driver is to go to device manager by click right on computer folder ..and in there select properties / hardware /device manager ..
In the list look to see the card reader .. if it isn't present click right on computer in the list ..and select scan for hardware changes..
It will scan and show all devices connected and with no driver..
If you are running windows 7 or vista you can try to select the reader when it appears in the list ..click right on ir and select update driver ..and let the windows look for a driver on line .. or select one in the list ..But the best will be to locate the exact driver and install it .
Also if all seam OK but the reader still would not work open it and check the connections on the board.. This card reader is plugged on a usb port in the board .. and it may have an issue with the connecter ..Or try to install the usb 2.0 driver cause if this is a 2.0 usb device ..it may be not seen by the windows without this driver ..