2004 Chevrolet Cavalier no heat coming out

What you're describing is typical of a leaking cylinder head gasket. Your mechanic can perform a chemical test at the coolant reservoir to verify that. That involves drawing air from the radiator through a glass cylinder with two chambers partially-filled with a special dark blue liquid. If combustion gases are present, that liquid will turn bright yellow. That fluid will no longer work if it gets coolant in it or if it freezes, so the car will have to be in the shop to do that test. In warm weather your mechanic can just run outside and perform the test in a minute or two.

That air will get into the heater hoses and prevent hot coolant from reaching the heater core. Don't worry about that yet until the other problems are repaired. You'll want to consider getting that red Dex-Cool antifreeze out of there too.

Do you mean the chemical test is a valuable one or that the test passed on this car and doesn't indicate a leaking head gasket?

Rats. The combination of symptoms points to a leaking head gasket. Do the radiator hoses get hot? If they do, and the heater hoses don't, that would point to a plugged heater core. You said the engine doesn't overheat. Does that mean there are no symptoms other than the lack of heat?

I'm sorry, but it appears I overlooked your reply. Have you come up with a solution?