Why doesn't the voltage drop across the resistors of my battery charger follow Ohm's law?
I don't seem to have enough reputation to comment, but something seems off. You're reading 35V across the 8 ohm resistor? 

This would mean from ohms law 35V/8ohm = 4.375A. so something is off if you're producing too different measurements. in other words, for 3.5A to flow through the resistor, the drop would be 3.5A*8ohm=28V, but you're seeing a drop of 35V. 

So for some reason I can only think the current measurement is faulty... Can you maybe explain how you're getting the 3.5A and 35V reading. Could you place a multimeter in series with the circuit and measure the current through the resistor if the 3.5A reading is from the PSU.