Question about N-channel MOSFET turn on Voltage
I'm going out on a limb and say you have your circuit backwards. Typically for an N-channel mosfet you would put the voltage into load then connect the other side of the load to the the drain. The source would typically be connected to ground. That way your Vg is always referenced to ground so your Vgs is whatever your Vg is so to speak.  Of course you may be doing something creative I don't understand.

As it is, any voltage you apply at the source will certainly show up at the drain minus the diode drop of 0.7V. This is when the MOSFET is off

I think if you just swap your drain and your source on the DMN3404L you should be good.