P0700 means the transmission control system has informed the Engine Control Unit (ECU or PCM ) that an error has been detected and the PCM turns the Malfunction Indicator (MIL) on.
As to 70-03, I am not sure what you are referring to as different code reader/scan tools would have different codes. I need the ODB-II code, as this is universal) to understand the problem.
The shaking and self accelerating should be due to engine surging when the idling speed moves up and down when transmission is in neutral. That could be due to insufficient coolant in system, fault in the idle control system or dirty throttle body and IAC.
Let me know of all the ODB-II codes and we shall see what we come up with.
Tuesday, April 19th, 2011 AT 8:32 PM