Heater blows cold air - help!

After a running a bunch of searches and doing some testing, here's what I have:
1. Little or no heat from the climate control system. Fan blows cold air at max speed when I set the set point to anything hot like 75 - 85 degrees.
2. All of the levers, rods, and flappers appear to operate correctly in the climate control system.
3. The diagnostic check (the "hold the Auto and Off buttons while ignition is turned on" test) resulted in no trouble codes.
4. Normal coolant temp on the instrument panel gauge.
5. Last fall I replaced the radiator and thermostat and installed a Prestone coolant flushing tee and flushed the system. After this was done I noticed that I had no heat. I've been living with it this way ever since, but enough is enough.
6. The heater core inlet hose (passenger side) is hot but the outlet hose (driver side) is cold after 15 minutes of driving. This seems really wrong to me, obviously. And get this: when I take the cap off of the coolant flush tee (which is installed in the passenger side heater core input line) I get no coolant flow when the car is running. It seems to me that the water pump should be pumping coolant into the heater core, right? At least enough to squirt out as I remove the cap. I see coolant there (and it's hot) but is just sits there without running out even though the engine is running. But the car isn't overheating like I think it would if the pump is failing, then why is there no flow into the heater core - and why is that hose hot if there is no pressure?

I'm confused - I think my brain is frozen. Any ideas? (About the car, not my brain)

Thanks,
Chris

[svx_commuter]

I think that when you did the flush the heater core got plugged up with crap. I suggest you try removing the heater hoses and flushing the cooler backwards to remove this stuff. I hope your core is okay.

I thought about the heater core being clogged too, but I'm confused about why I have no pressure on the supply side of the system (where I have my flushing tee). When remove the tee's cap I don't have any coolant squirting out, even though the engine is running. Am I correct in thinking that the passenger side is the input (supply side) of the heater core? I guess I'll just wait for a warmer day and unhook stuff and try to blow it out.

svxcommuter, you were right. The heater core was plugged up with junk. We finally had some warm weather and I flushed the core - I now have heat! Thanks.