I don't know if this will help you or not but I had the same problem with my 92-940 just last summer. I just bought my wife an 850 so I don't know if the system is set up the same way. Here goes.

My 940 had the exact same symptoms that you describe your 850 having. I did all you did and bypassed everything using a paper clip at the evaporator. I finally got tired and called the dealer and talked to the tech supervisor and explained my dilema. Behind the glove box (that I had removed) there was a hot lead that went to the dash switch which turns everything on. I found (with a test light) that sometimes I would not get power to the switch assembly. The tech supervisor told me that the black lead that feeds that switch is behind the glove box and that it is a white clip (the kind that snap together) connector. He told me to look inside the connector because the connection is usually cooked on the inside of the connector and you can't see it unless you try and separate them by pulling them apart like you're trying to disconnect them. Sure enough, it was cooked and all I did was hard wire it with a wire nut, no more problem!!

Hope this helps you.

Henry

97-850/76k,92-940/224k, 91-740/178k.