Sounds like you're not getting 3rd, maybe 4th (OD).
When did the fans stop working? Same time this started?
Any other weird electronic symptoms? Anything at all?
How are the terminals on the battery, are your power and ground wires clean and free of corrosion? You haven't by any chance had to get a jump start on the car lately, have you?
Sometimes, a bunch of seemingly random electronic part failures can be traced back to bad batteries, battery wires, or the connections at the ECM/PCM. The PCM depends on a good solid ground to make a lot of things work right. If the ground or power to the PCM is even a bit sketchy, a lot of things can seem to go nuts at once.
I believe your PCM controls the fans. If you put your HVAC controls into defog mode (or command A/C from it), the compressor should kick on, and the fans should turn on, no matter what temp it is outside.
I'd start with checking the battery wires, and cleaning the terminals. Go through the PCM connector and check the pins for any sign of corrosion. Unplug the battery and clean up the PCM connector.
This is all just generalized stuff. I don't have much experience with this year, or the electronics specifically. But its somewhere to start. If none of those things help, maybe some of the gurus with more experience with cars like yours can be of more help.
2004 Buick LeSabre Custom FE5 GXP suspension conversion. 170Kmi
2001 Silverado 4WD 5.3L, 33" BFG ATs, Z71/Z82 pkg, 147kmi.