I have a 1996 BMW 328is with about 120K miles on it (yeah, I know, a lot of miles, but hey, it's the ultimate
driving machine, not the ultimate sit in the driveway machine). A month or so ago, my climate control computer began to
turn off intermittently -- but it would leave the AC compressor engaged. The AC light on the AC button would remain lit, as would the air vent button (whichever one had been last selected), but the display would be dark, and hitting the buttons did nothing. So, you would have the AC compressor on, but no fan.