When the Transmission Computer detects a problem, it goes into "limp" mode which makes the transmission stay in second gear. That is only to allow you to drive the car slowly to a repair shop without needing a tow truck. There is going to be a diagnostic fault code stored in that computer. Having that read is the place to start. Many auto parts stores will read codes for you for free, but they usually can only read engine codes. You may need to find a mechanic with a full scanner to read transmission codes.
Given the additional symptom of no speedometer, the most likely suspect is a failed speed sensor. There's two of them; an input speed sensor and an output speed sensor. Both are used to calculate road speed, and a failure of either one will send the system into limp mode. You have to turn the ignition switch off and restart the engine to get it out of limp mode.
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Sunday, June 15th, 2014 AT 8:04 PM