Four hours later, and my Mac Mini has a running 500GB HDD now. Yay.
What took the longest was copying all the data off of the old drive to an external drive then back on to the new drive once installed. This was easier putting the data back on as the new drive is a 7200 rpm drive and the original drive was a 5400 rpm. Almost 200 rpm makes a big difference.
I think that this is a band aid until I get a new Mini when the next generation comes out. Rumors abound of a Mini with a HDMI port. If only there were words to describe how exciting that is to me.