Determining node voltages and ladder currents in R-2R DAC Ladder with Op-Amp
The switches are connected incorrectly. There should never be a possibility that the ladder resistors are not connected to anything, which is what I see in your schematic. The switch needs to be connected so that the ladder resistor is either connected to ground or to the reference voltage at all times.
For me, the easiest way to analyze an R2R ladder is with superposition.