Hi ThatDood,
The battery cannot supply enough current to make the LED sufficiently glow. The hindrance here is the high resistance of the thermistor. Increasing the value of the shunt resistor to 4 kΩ is inadequate, note that by removing it (increasing the resistance to ∞) the current could not come too close to 1 mA. Check the On current (ION) of the LED from its settings.
If you want to make this simple thermal sensor work you have to find a way to lower the resistance that limits the current from battery. Otherwise you need to find alternative configuration. Another important concept to consider when trying to make this circuit work is self-heating. Ideally, the change in resistance of the thermistor should depend only in the change of the temperature of the surrounding or the object the thermistor is having contact. If you supply the LED current through the thermistor, the transducer itself will heat up due to current flow. This will have significant influence in the change in resistance of the transducer thus causing deviation of its response from surrounding temperature.
Of course you may also consider using transistor(s), op amp, or comparator.
Best regards,
G. Goodwin