I'm still not really understanding your idea. You could use 4 wires each as one bit but that wouldn't handle multiple pushbuttons simultaneously and you would require a seperate power supply in the other room. This is what I had in mind:
View attachment 38149
There's 2 PICs each less than $2, 8 resistors mayby .05 each, the LCD, and the pushbuttons. In the finished circuit you'd need a few caps here and there and maybe some pull up resistors on the I2C lines but that's about it.