update on previous post, 3100 getting hot

well i was able to check out the 95 cutlass for myself and i found that the coolant temp sensor was broken so i went to autozone and bought one and installed it. i made sure the car had antifreeze and i went to start it and before i started it i noticed the temp gauge was pegged out on 260 or 280 whichever it is, and i went ahead and started it up and as soon as i did the HOT light lit up. does anyone have any ideas as to what would cause the gauge to stick or the hot light to light up? I let the car run for about 10 to 15 minutes so that the engine could warm up. i checked the top and bottom radiator hoses and they were both cold.i felt of the engine and it was hot. So i am sure that the thermostat is stuck but would that cause the gauge to stay pegged out?
when i started the car it did turn over quite a few times before it started. and it was like this all 4 times that i started it up. sorry for the long post just wanted to give as much info as possible, thanks for the help any of you guys can give.