2004 chevy 2500 6.0 it has the powersteering and hydralic brake booster system

Hi,my rear heater is blowing cold air.I took it to a shop,they told me it's the heater core,so i change it,a $ 300 job.
But it's still not working all the time.They told me to press on the gas pedal to send hot coolant to the back for it to work but still it's not working.Does anyone know what's wrong with it?
Winter is very close now and i have small kids.i would really appreciate if someone could help.

I'm looking for a replacement power booster and I don't know which it is. When looking up parts it's states for use with a particular JH system. How do I find this? I have a 2004 Chevrolet suburban 2500 4x4 6.0l.

abs and brake lite come on and stay on,ac blower also stopped

What is the easiest way to change cabin air filter

Can I run E-10 fuel in my truck.

on my 2004 chevy suburban 2500 the power steering quit working at the same time the power brakes quit working is this the pump because if my hydroboost went out i should still have power steering right

My parking brake indicator light is flashing, and the warning signal is beeping, even though the parking brake is released. Any suggestions?

Where is the fuel filter located?