110 on the gauge is NOT overheating, its to be expected the temp will creep up if the car is not moving. the fan should cut in around 3/4 on the gauge and keeps going till temp gets to around 1/2. the blocked pipe is definitly NOT normal though, so fix that. If the fan doesnt come on when gauge gets to 3/4, then it could be the fan switch. Have you tried bridging the pins on the fan switch plug? bridge the red wire to each of the other 2 pins in turn, and fan should run slow & fast.
if the warning light on the dash goes off, that means either car is overheating or coolant level is low.