2000 Chevrolet Silverado 5.3 overheating drove vehicle to work and blew the top of my radiator. So i replace the rad. And thermostat thinking that's my problem. Bleed the system turn on heater in vehicle waited to get heat no heat at all bleed system again. I revved the engine: nothing. Could my heater core be causing my overheating problem?
My guess would be the water pump is broken.
This would explain why you aren't getting any heat; the water pump isn't pushing hot coolant to the heater core.
It would also explain why the engine is overheating even after you replaced the thermostat; the water pump isn't pushing/pulling enough hot/cold coolant out of/into the engine
This should be easy to test. When the truck is cold, start the engine. The thermostat probably won't open for a couple minutes, so the water pump will only be pumping coolant to the heater core. Locate the heater core inlet and outlet hoses on the firewall (probably to the left of the engine?). Unplug both hoses from the heater core. If the water pump is working fine, the hose which takes hot coolant out of the engine will start shooting coolant everywhere.