Thanks for your reply Steve.
I got it working!
http://youtu.be/xoxdGcm2wikI did try to use the Brilldea design as a baseline. That is where I got the idea that I needed some capacitors but I was not sure where to put them. My total lack of understanding was absolutely no help

I did get the lights working though. I read Grumpy Mike’s page about De-Coupling and tried to implement that the best I could but in the end my problem was something else I learned from Mike’s power supply page that really fixed the problem. I simply needed to have the 12V supply and the 5V supply share a ground. That fixed it.
I am still confused about the capacitors because it works with or without them. But my understanding from Mike’s page is that they will help the overall consistency of the design.
Thanks for your advice about the ebay deals. I think you are right. All Brilldea sent me was a long string of lights that I had to cut up to add (hack) connectors to. I am sure the ebay products are similar. I can say that I am a HUGE fan of this kind of LED. They are really bright. I was trying to create my project with an RGB LED matrix and that was way to much work for the minimal light intensity.
Now my next power related problem is that I want to create both a 12V and 5.5V regulated power supply from one cord. I need to split the power to supply both the low voltage boarduino and the 12V leds. I think I ‘understand’ the voltage regulator circuits necessary but I am not sure if I need to use a 24V supply and then break up into 12V and 5.5V supplies or if the single 12V supply can handle both power supply circuits. I know that this must really expose my lack of basic understanding but I am simply fishing for clues so I know what to search for. Any ideas?