Switch 12V and 24V low current load (LED button) with 3.3V and 5.0V arduino
Based on your schematic which should work wonderfully , there can 4 issues. 


The mosfets aren't suited to logic level control.
You didn't wire it as shown. 
The mosfet are damaged. 
Your code is wrong. 


If you wire the led and mosfet to power and tie the gate to ground, does it turn off? If you tie it to 3.3V via a 1k resistor does it turn fully on? What is the resistance of drain to source when gate is at 3.3V?

You can avoid mosfet issues, replace it with a standard small signal npn  transistor, like a 2n3904. 1k base resistor is enough art your load current.