Something doesn't look right ...
Your "Apricorn SATA Wire Notebook Hard Drive Upgrade Kit" is intended for laptop HDDs. These HDDs are powered from the USB port and are 5V only.
The Dell Optiplex GX520 is a desktop machine. The HDD in that machine would be a 3.5" model. Desktop HDDs require 5V and 12V and therefore cannot be powered from a USB port.
If this is a 3.5 HDD, the adapter can't provide enough power to it.