With 20k you wouldn't even be able to design one custom chip.
He wouldn't need to go ASIC. Use an FPGA, and none of it is impossible. Basically a console shaped Minimig board with a PowerPC upgrade slot from the sounds of things. FPGA-Arcade may already satisfy the majority of all that. For a livingroom console, for a handheld console then he'd have to do a new board, and it might not fit a PPC addon.