Can my computer handle this GPU upgrade?

You may need to disable the on board graphics in the bios settings. You'll see a quick flash at start up that says something to the tune of "Press F2 for setup" you'll have to flip through the settings and look for a setting to dissable the on board graphics or set the graphics to only the PCI Express. Save and exit the BIOS, shut of the computer and attach the monitor to the new card, when windows starts up the screen resolution might be pretty messed up because it will be using a genaric driver until you install the proper one off the CD or through windows update.