Flushing the heater core
 

I think that's my problem based on other threads.

Question is - to do this, do I have to take apart the entire dash? Because for one, I don't know how to and two, a mechanic would charge a FORTUNE for this.

No you don't have to take apart the dash, as there is no real need to take the heater core out of the car.

Look at this picture:
http://www.hondapartsdeals.com...8.png

The two longest/largest hoses leading out of the heater core, lead to your engine. So, disconnect the sides of those hoses that are nearest the two "E-15" labels. Then, with your car set to full heat (inside the cabin, since it controls the valve leading coolant into the heater core), push water through the valve side of the heater core hoses (top left in that picture). You should get fluid out of the top right hose.

Re: Flushing the heater core (Revolver123)
 

you can buy a kit cheap at autozone... for backflushing,

(attachments for your garden hose)

Re: Flushing the heater core (RISRdotNet)
 

Be careful with these kits tho.. their easy to use and seem to work for the most part.. but i did it when i had my dakota... and maybe a week later my heater core went out... it started blowing smoke into the cab.. and leaking on the passenger floor... i don't know if the 2 are related but hey it's worth a heads up..