It's brand new, in fact its never actually been used. My problem is twofold: the fuse for the heater blower motor keeps blowing out. It will work for a week or so, then the fuse will blow and I get no heat (or A/C for that matter) till I replace it. But even when the blower motor is working, I don't get heat. The core is fine, no leakage or anything, and I can touch the heater hoses and feel the hot coolant going into the core. So what's the problem here? The core gets hot, but the heat doesn't reach me. I've heard of a 'heater control valve'... what is it, and could that be my problem?

MrJ,I have had similar problems...here is my experience on this. Assuming all the hoses are connected to the heater core correctly,and you once had heat,the heater contol valve is most likely good(not stuck open or closed) if you feel flow to and from the radiator. It is on a vacuum feed so check the vacuum here or rule out the valve beeing stuck by getting a new one(relatively cheap). On a stock TPI motor it looks like a round dial right above the passenger valve cover with 3 hoses and a vacuum line which run into it,can't miss it. Blowing fuses is obviously not normal,is your blower motor causing the blown fuses? You may need to replace the blower,but most likely the wiring is shorting or grounding out. I'd check all wiring for continuity and volts at the blower,ground and the wiring to the hvac unit itself as a start.
Once you have ruled out the blower and wiring,the cooling system is a relatively basic system...if it flows it usually will heat. Assuming you have a stock thermostat that is operating correctly,check your cooling systems vacuum lines...no vacuum,no heat. Another cause of the problem could be your vent door connected to your hvac controls. When inside the dash,look at the main vent door,these sometimes can get obstructed with foam and other material which prevents the venting door from opening. I've had this problem as well as my slider control not properly pulling the vent door open.
If all these check out,one of the most important things to your heat system is trapped air. Does your car overheat,when the core was replaced did you burp the system? If the heater core or any other work has been recently done to the car,the system needs to be burped. Trapped air in the cooling system will prevent heat every time. If this is a possibility,start the car with the rad cap off,and turn the heat on. Wait and watch for trapped air to bubble out of the radiator and top off when the engine is at normal operating temp,close system. This is another visual way of inspecting the system to see if your stat,cts,and fan switch work properly and create coolant flow inside the radiator.

Hope some of this helps,I've had the same problem a few times and have seemed to get it to work each time.Good luck.

Niko

I had no heat on my GTA when I replaced the heater core too. Turned out that the motor that operates the cold/hot air flapper thingie was shot. I yanked on the steel rod to manually close the door and now I have heat. I don't think the non digital dash cars have the motors operating the doors, but that doesn't mean that the door is jammed open or something.

ive seen this many times before...maybe an air lock...just bleed the hoses