I forgot to mention: the a/c is starting to go out too; it blows cold for a few minutes and will then get warmer, and goes back and forth. I have heard that the fan in Saturns are connected with the A/c in some way. In this case, I'm wondering if the fan is good but the A/C might be causing the problem?
Your A/C behavior and heating up at stops are fully consistent with the fan motor not operating at all.
Indeed, the fan is designed to kick in when the A/C is turned on and should be running whenever the A/C is running. This helps cool the condenser when the car is stationary, thus keeping the A/C air cool when the car's not moving. Same goes for the radiator if the engine gets hot enough, thus explaining your heating up at stop lights without the fan kicking in to cool things back down (fan should kick in at 3/4 tick)
So the fan is not kicking on when it should (at all). The question is why not....
Normally I would start with replacing the ECTS which measures coolant temp but since yours does read right into the red zone it appears functional in the right ways.
Next to check is the relay. Swap it with the identical one next to it (the A/C relay, which we know is good since the A/C kicks in) in the underhood fuse box. Try to turn on the A/C. IF the A/C comes on, then we know the cooling fan relay itself is good, since it operates in the A/C relay slot just fine. If the A/C doesn't come on, then the cooling fan relay was bad and needs replacing.
Another quick test is to disconnect the connector at the fan and briefly wire the terminals straight to the battery (and ground) just long enough to see if the fan spins. If it does not, the fan motor is bad.
It is possible but unlikely that the relay AND fan motor are both bad --- so diagnose in the order listed above......(relay, then fan motor)
Thanks a lot, Derf! Your advice was right on target, and I don't think anyone could have put it more clearly! You saved me about $250. It was the fan which I bought for $40 and was able to install in about 2 hours. I'm new to doing my own car work so most people could probably do it in a few minutes.
I found this video on youtube, but there was no way I could take out the fan in 5 minutes :