Individual Digital Control Of LED Array
The WS2812 series of LEDs with built-in controllers may be a very simple solution for your application. They are most often seen on the LED strips / rolls and in that format come with a controller.

Each LED is connected to positive and negative supply and a data line is fed in one side of each chip and out the other to the next chip. A string of pulses is sent to the chain and each chip accepts 24 bits (8 red, 8 green, 8 blue) and then passes on the remainder of the commands to the next chip. The result is that the hardware is very simple and the complexity - which isn't too bad - is in the code (where you're unlikely to break anything).

There's a tutorial (I'm not sure how good it is) over at Arduino.cc that may be an easy way to get started but if you can't figure it out then do a web search. The devices are very popular.