All prior posts before this one are posted in our community profile, not on this specific project, sorry for being so lazy to proper handle your site's interface.
Our circuit uses 4 'AA'/small batteries, we used specifically rechargeable or old batteries to make sure that voltage never goes above 5.3v, we could go further, but since we have used low resistors to maximaze led's output, if we wanted something more compatible with standard batteries we would have used a little higher resistors.
Our final array board is 4x4 leds/switches, while the original project was meant to handle a 10x10 board, we were not able to buy those in time (we are still waiting for it on the local supplier), since we bought all switch+leds parts on the store and did not want to place 2 different kinds of leds/switches. A good idea is to use monome's switches for that, that will do just fine.
I hope you enjoy that just as much as I had cried and got pissed when things stopped to work while in the development of it ;-)
Last, and likely least, the picture with the circuit overview and comments, where you read "Pull-ups!" are, in fact, current-limiting led resistors, they are quite low (130ohm) and depending on the manufacturer of the IC employed it may overload the output (fan out) of the shift register, our worked well, got a little weak when all outputs were on, but since most of the time it will not be full-on, we thought that that was an okay behavior, still, for textbook circuit building that is wrong (and it is the reason why we don't recommend you to use 1.5v batteries on it, it might burn the leds).
Our circuit current consumption floats around 110mA at 5v (5 leds on), thus we can operate it quite a long time before recharging the batteries.