The key here I think is the NAND. I know you can do practically anything with only NAND gates. But without it, and with just control structures, I don't think there's a way to perform computation unless there is some theoretical voodoo withcraft possible, something like nop-padded cellular automata given the infinite memory. But I don't have any qualification to talk about this, I'm just some random dude who flunked out of the university but finished all Zachtronics games.