Thought I would start a new thread on this...didn't see one while searching my model year/make.

Original reply/post is in Accord/Crosstour 2003-Current.

Had the same problem with my 2000 Accord a couple of months ago, but only the fan would work on high with no a/c, heat worked fine. Since my son drives the car for school/work, and in between my job, it took me a while to investigate.

Fast forward to today...my 04 Odyssey just started doing the same thing! Now, since this is my wife's ride, I had to work on it pretty fast. I checked the threads on this site and decided to buy a refurbished blower resister (thx justinsbg!) to see if this does the trick. This was the cheapest option for me.

I'll keep you updated as soon as I install the part. My fingers are crossed.

Btw...the location of the resister (04 Ody) is the front right (passenger) below the glove box. No need to take any other part off to access it. I'll post pic later.
My 2000 Accord resister is the same part and same location (V6 model), which was a very pleasant surprise.

 

You're lucky, most of the time you gotta pull the dash to get to it.

 

Ok, sorry for the long delay on getting back with a solution...
Received my resister part, installed it and it works just fine.
My symptoms for this situation included...fan only works on high, a/c does not work and heat works. If you have these 3, then it is probably the resister. If you have only one of them, then it may be something else.
Also, this is the original resister, so after 13 years, I guess this is something that can go out 'naturally'.
I tried my best to get photo, but couldn't get a good one. The part is trianglular with three hex nuts/screws. Again, the part location is in the forward right side of the passenger feet area.

***UPDATE*** 4/15/2014
Parts still working fine on both accord and odyssey. Heading into summer months....keeping fingers crossed!!!!