I attempted the Loop-Back Test but could not complete Step 6 because the arduino is not being recognized by my computer. When I try to open the serial Monitor I get the Error "COM 4 not found", and as I mentioned before the "Serial Port" option in the IDE is greyed out so I can not change the Port #. As before, the Uno does not appear at all in the control panel. Additionally, no "unknown devices" appear in the control panel.
After leaving the Uno plugged in for 5 minutes nothing on the board becomes hot. :S
Do you still suspect a broken Chip?
Cheers & thanks for your response 
-Tommy