Saturn SL2 says it's overheating?

[Houston]

I have a 2000 Saturn SL2 with a 4 cylinder DOHC that is having some cooling issues. A couple of weeks ago the coolant lamp turned on; I didn't think much of it, because the car didn't overheat at all and it ran fine. Today, I started my car to go to work. As soon as I started my car the temperature gauge shot all the way to hot. I repeated this process a few times when diagnosing the car, and every time, when I start the car, instantaneously the temperature gauge goes straight to hot, even if the car is cold as a coors light.
I figuired it was most likely the engine coolant temperature sensor. I replaced it. The temperature gauge when starts still goes right away to hot, which has to be a false read, because its 40 degrees here. and when I first put the sensor in, it couldn't have been much warmer.
If it were the thermostat, wouldn't it be a gradual raise of temperature because the water in the engine still needed to be heated up, instead of a instantaneous hot reading?
The coolant level is fine. I inspected the hoses, and they appear good. not crimped. Also the water pump is not leaking. The serp. belt needs to be replaced, but the water pump is still turning, and if it were the water pump; wouldn't it be again a gradual raise in temperature after the car had been sitting in the cold for so long?
The coolant fans are not turning on, even after the car idles for 10-15 minutes. I collect that the fans should turn on immediately, given that the car thinks it's burning up from the get-go. Tomorrow I will jump the fan motors, and try to solve that problem.
There is a check-engine light on, it has been on for some time. This is also something I will check tomorrow. The car still performs very well, and this is the only problem it has had while I have been driving it.
Any help would be appreciated.
PS could it be possible that it is bad wiring? What circuit would it be on? I wrench on cars, but I am not an electrically inclined mechanic, If anyone thinks it is wiring related, please give me some pointers. Thanks!

[Otto]

Please remove all the unnecessary chatter and resubmit the question.

[sterling m]

That check engine light could be seeing a fault in the wiring for your coolant sensor , but there are hundreds of things that can set those off. Could you possibly get a cheap gauge set ( sensor and gauge ) and wire that up , even in a safe place under hood, to see what is really going on . You could have a toasted wire or a bad ground on the gauge , etc. etc. Good luck .