AC problems with our 2004 Honda CRV

The AC in our 2004 Honda CRV works fine as long as it’s only turned up about halfway. When we turn it up higher than that (and we’re on the highway) the cold goes away and we start getting only the fan. On a hot summer day in South Texas, it’s VERY obvious when this happens.
The Honda dealership here in Corpus Christi says that we need to replace the “Heater Control Panel” which would cost $798 for parts and labor. I asked how they knew that was the problem and they said that they hook it up to something and go step by step checking the system until they get to the problem … Our heater works fine and the AC actually works fine, as long as the fan is only half-way on. So I’m wondering if there might just be some relay switch or something that needs to be replaced, instead of the whole Heater Control Panel, since we would prefer not to spend $800.
Hope you can help! I’ll be listening on Saturday morning, in case Clink and Clack want to call me …

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I’d suggest that you get a second opinion from a shop hate specializes in automotive AC.You’;; need to go to an AC shop anyway to get the system recharged.