The engine never warms up because both radiator fans stay on!

Look for any obvious wiring problems , the fans running all the time may be a " fail safe " thing if a circuit is open like if the gauge is broken somehow , check any applicable fuses ,. Mice can invade even a daily driver .

Sounds like a problem with the coolant temperature sensor or the wiring going to it. Has the air conditioning stopped working too? If so, that's definitely what's going on. When the computer stops getting a signal from the coolant temperature sensor it assumes the engine is overheating and takes steps to prevent engine damage. The radiator cooling fans will run all the time at high speed, and the air conditioning will be disabled. The temperature gauge on the dash will usually stop working too because the coolant temperature sensor is also the sending unit for the dash gauge. The check engine light will usually come on as well. Hope that helps! Jim

One other thing, the new coolant temperature sensor should be an AC Delco sensor. For some reason GMs don't like aftermarket sensors. Jim