First, please make sure your card reader has the right slot. Sony memory cards are "Memory Stick Pro", or M2, as most call them. They do not fit in SD card slots (as they are a bit thinner) and need a card reader with a specific slot.
This considered, make sure the card reader is properly installed. For that, launch the device manager (start>run>devmgmt.msc, or just type device manager on windows 7 and above).
In the device manager, you should see the sd card reader listed under the USB controllers. It may be be named Generic USB Hub. If you do not find it, you probably have a hardware issue.
If anything under the device manager presents a yellow sign with an exclamation mark, it means some piece of hardware is missing a software driver and is not working properly.
Please tell us if you find anything unusual there.
Most commonly, a card reader not working means a missing driver.