I have a work computer (HP Pavilion s51114 slimline) which is only a year old. It has the Intel HD family graphics card. It already has the one monitor hooked up to the DVI connection on the tower, and the only free connection is the VGA port. I was wondering if it is possible to buy a VGA cable or a converter from VGA to DVI, and get a second monitor to use for an extended desktop (not a mirrored)?
You absolutely can do that. your second monitor should have a VGA port in the back(Most or all monitors do), just simply plug a VGA cable from your monitor to your PC, your second display should automatically be detected in Windows. If not, simply go into your display settings and tell Windows to "extend display" to your second screen. the only difference you might see is the picture quality as one is Analog and the other is Digital.