The nearest symptom I could find which sounds a bit like your fault is described below, but your first step is to find what fault code has activated the service light.
Trans does not up-shift out of first, speedometer reads zero at all times: VSS failure. Easy fix on rear of transmission, but cross member must come out to access VSS.
This relates to the 4L60E transmission so you would have to make sure yours is that model i am not sure what year they began using it I think the "E" stands for electronic.
The clue which points to the speed sensor (VSS) is you having no speed reading, it could be a connector. If the above description sounds like your fault this sensor and it's wiring would be the first place to look, it's mounted on the rear of the transmission on the transfer housing.