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The P0700 sets in the engine controller any time a code is set in the trans controller. This code is merely informational and doesn't point to a problem. The code relating to your check engine light and the trans not shifting, and the speedometer not working is the P0720. This is for the output speed sensor on the trans. This is mounted on the front of the trans and wired to the trans controller. It's signal is used for shifting control, but it's also converted to vehicle speed and sent out to the other modules, one of them being the instrument cluster to run the speedometer. This could be caused by wiring, the sensor, or the trans controller. A failure of the sensor itself is pretty common. They run about $20 at a parts store and are easy to replace.