Car dies after it warms up, no pressure in radiator when i remove cap, and acts like it's starving for gas

It does not circulate until the engine is warm. At that point the thermostat(cooling valve) opens allowing the coolant , from the radiator ,to circulate into the engine. Before that point only the coolant already in the engine circulates, inside the engine alone. .

I would try a crank sensor

Some of the information does not correlate.

If there is no Pressure, then you Radiator Cap is Bad

Stalling or Starving for Gas can be a Fuel Pump or Air Filter

Remove the Air Filter and see what happens.

Test the PRESSURE of the FUEL System

try buying a new gas tank cap at walmart.

I agree with Dennis on checking the fuel pressure.
Could be a bad pump, restriction in the tank, vent problem in the tank, bad fuel filter, or bad pump relay.

CHECK FUEL PRESSURE AND CALL ME .985-248-2726

most likely fuel filter, pump or clogged injectors. Check for pressure in fuel rail at valve on rail.

remove the radiator cap and let the car run for 30 minutes to let the air out of the heater coil, these radiator caps on the 2008 Impala will not bleed off, while running notice if air bubbles air slowly rising to the top of the radiator cap, re-install cap and see if this fixes problem, we also purchased a new radiator cap, this fixed my wifes car.

possible blocked fuel filter or fuel pump not supplying enough fuel (starving) check fuel pressure with pressure gauge
also blocked exhaust or cataletic convertor can cause same issue

Have you tried replacing the pick-up coil?