Problem with the Battery discharging circuit

[Harneet]

I have a circuit that aims to discharge a battery and hence monitors it's voltage.
The circuit either drains 4 uA current through a 680k resistor or 20mA current which is driven by the DAC. The switching between these two scenarios is done using a 74hc125 ( have tried N FET as well)

The circuit diagram is attached.

Problem: When the switch corresponding to 680k is enabled it gets grounded but when switch corresponding to 10 ohm resistor is enabled it doesn't gets grounded.
I'm unable to spot the problem with the circuit as I'm very naive in electronics.
Please help!!

[tree]

If you're measuring the voltage at the "grounded" terminal of your 10ohm resistor you have to remember that you'll have some voltage drop across your transistor that's inside your 74HC125. What's the voltage when you measure at the output of each channel of the 74HC125?