If I remember, you wanted a few different groups of LEDs, right? Is that ALL of them...the 24 in schematic?
Which ones are going to which group?
Which need to be controlled by switches?
No more help from Osgeld?
This may not be very helpful right now, but....
Looks like your gonna need to 'shiftOut' 24 bits at a time to turn LEDs on/off. That's a series of 24 1's & 0's....in the same order as the lights. '1' for on, '0' for off.
With this arrangement, the "easiest" way to approach it (I use that term loosely) would probably involve a lot of bit wise operations. http://arduino.cc/en/Reference/BitwiseAnd
Use "random" to generate 24 random bits to produce your random pattern...
Assign a certain bit location to each switch –
00000001 for right most switch on
00000010 for the next one on
00010000 for the far left switch on
Then, 'add' or 'subtract' that bit to/from the random pattern depending on if that light should be on or off.
Do you have the hardware put together yet?
If so, find some shift register examples, load 'em up, see what they do. Then, play with them to make them do what you need.