Better Transistor Inverter Using Ground Signal?
I think there are two transistors too many.  Most people will say that 70K is a bit high for the base resistor in this application, but we can leave that alone for now.  Here is a more simple solution.







simulate this circuit &ndash; Schematic created using CircuitLab

Is there a reason you are not using a saturated switch to drive the LED?  Also, why is exactly 10 mA LED current important?