Background: Last year, I had a new condenser installed and the A/C system converted to some hybrid refrigerant like 134A. It cooled all last summer and this one just fine, up until about a month ago. We had heat too, and all buttons worked as they were supposed to, including blower speeds, flaps, etc..
The Problem: At seemingly random times, after starting the car, nothing happens from the system. None of the buttons will do anything, the blower doesn't function no matter what button is pressed, or where the temperature wheel is set to. In other words, no heat or A/C. If you press the buttons, you can hear flaps opening and closing, so I suppose the vacuum lines function.
So we go to the mall or whatever, turn it off, then awhile later, on startup, everything comes to life again! A/C or heat depending on what the temp wheel was previously set to.
I'd thought that not turning it off (far-rightmost button) would 'fix' this, as it seemed to return to normal on startup if the system settings were left alone, but alas, it failed twice to come alive yesterday and the off button hadn't been touched.
Does anyone have an idea what system component(s) is/are the likely cause of this erratic behavior?
I checked the OVP relay and the fuse is OK. Likewise all the fuses in the box. It does blow cold air when it works, so I assume the charge is still up to proper level, and the blower motor works on all speeds, again when the system kicks in.
I don't want to waste my time or money chasing down every possible source, but would appreciate a few pointers on what would be the 'top of the list' things to test.

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1986 560SL
2002 Toyota Camry
1993 Lexus