8x8 LED Matrix re-build
I doubt there is an IC out there just for controlling 64 lines in a grid pattern. 

Now, since you mentioned things like the Mux Shield, Arduino, and Pi in your question and comments, would 8 shift registers be sufficient? I know that this would work because I actually built a non-multiplexed LED array using 8 74HC595 shift registers and 64 individual wires to each LED (hand soldered, it was a lot of work). It was driven by an ATmega328p at 16MHz and there was no noticeable lag in the screen update.

I know this is not the ideal way to control an LED array, but given your situation of 64 individual wires, I think shift registers would be a feasible, and possibly the only way forward.