2N7002 MOSFET gate voltage internally being pulled high, potentially dead
Seems like you've damaged the gate of Q2 by ESD or similar effects. It's a bad idea to expose an unprotected MOSFET gate to external connections, particularly a small MOSFET such as a 2N7002. 

A series resistor (eg. 1K) and something like a 5.1 or 6.2V zener from gate to source will protect the MOSFET from most reasonable transients. 







simulate this circuit &ndash; Schematic created using CircuitLab

You could switch to a BJT (with a series base resistor) but it would be a good idea to have a diode from base to emitter to prevent ESD-induced reverse base-emitter junction breakdown, so the component count does not look much different.