Although this is an old thread, this is the exact problem my 1999 Odyssey LX with manual climate control just had. The Blowers (front and rear) worked on every speed setting, the AC compressor and all LEDs on the vent/AC/Recirc/Defroster controls went out. This occurred once on a long road trip, I stopped, turned off the car, and upon starting it, all LEDs and AC worked. ...UNTIL the return road trip... when the AC was working fine then the vented air got hot, all AC/Vent/etc LEDs went dead and nothing would bring it back.
Since the blowers worked on all speeds, the problem is not the blower relay. I talked to my local mechanic and they agreed its the control unit but the technician was already booked and they had no idea how to do it. But he pulled the instructions up on his mechanic software and it's rated for 1.3 hours labor. Now the part search began.
This problem IS THE AC/HEATER CONTROL ASSY, Part# 79600-SOX-A03ZA for 1999-2004 LX with manual controls (not the Auto Climate Control). NJ Honda dealer #1 wanted $492.22+tx; dealer #2 wanted $428.08 (USD). Online mail order from various Honda dealers was $300-$328 + shipping where I looked.
I called a local wrecking yard/recycler/junkyard and they wanted $75+Tx=$82. Once they got me the right part, I put it in... ugh, the LEDs sort of blinked and I thought the unit was toast. Then I smartened up, disconnected the negative battery cable, left it for a minute, put the cable back on the battery, started the car and IT WORKED!. Needless to say, I'm psyched, my wife is happy we have AC for the trip this weekend, and I saved more than $500. Once I had the part it took all of ten minutes (really) to put it in.
Thanks for this thread -- I would be lost without ODYCLUB.
1999 Odyssey LX, 216,400 miles, tranny rebuilt at 174K, Tows a 2700# trailer in summer, fluids changed frequently