Why doesn't my MOSFET switch off?
MOSFET is "upside down" as Mike said.

BUT

3 "fixes":


Use P Channel FETs and all shall be wellish.   


FET will be on when gate is LOW (~= 0 V).
FET will be off when gate is HIGH(~= 4.1V) 




IF you can isolate the MOSFET 4.1V and gnd feeds from the rest of the PCB by cutting tracks then


Swap MOSFET 4.1V and ground
Reverse LED polarity






Depending on pads:


Take MOSFET

Bend leads UP  

Invert MOSFET - solder MOSFET D to old S pad

Solder MOSFET S to old D pad.

Solder MOSFET G to G pad.

Or use wire tacked on leads to make it easier.