The P0601 code means internal PCM failure; the only possible cause for this code is a defective powertrain controller. No external cause, including loss of power or ground, can cause this code. It means that the computer has failed an internal CRC Checksum test (data is not being stored correctly in memory).
You need to take the vehicle to a Chrysler dealer or an independent repair shop with Chrysler programming capability and have the PCM replaced. The vehicle will never run correctly untill you replace the defective PCM, and any test procedures performed with a defectice controller in the vehicle will likely yield inaccurate results.
This is not something you can do yourself, a the new PCM will not operate correctly untill the software specific to your individual vehicle and options has been programmed into it.
The P0700 code does not indicate any particular failure, it means that there is a fault code stored in teh transaxle controller (it is just a flag to indicate the technician should also look at the TCM for faults during diagnosis).
There may not be a problem with the transmission or it's controller; and diagnosis of that system should not be attempted untill the PCM has been replaced. Many of the sensors connected to the PCM (such as coolant temp, throttle position, and MAP) are critical for TCM operation as well, and information is shared betwen the modules on the data bus. If there is an internal PCM failure, some or all of the data needed by the TCM may be missing or corrupt, resulting in the TCM thinking there is a problem and defaulting the transmission to limp-in mode.
Step #1 before going any farther (or diagnostic results will be inaccurate) is to have the faulty PCM replaced and programmed...
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P0601-PCM INTERNAL CONTROLLER FAILURE
This symptom is diagnosed using the test P0600-PCM FAILURE SPI COMMUNICATIONS.
Ignition key ON.
Internal checksum for software failed, does not match calculated value.
The Transmission/Transaxle Controller monitors the malfunction of sensors and actuators relating to Transmission/Transaxle Control. If any malfunction is detected, they inform the PCM by sending a signal - By illuminating the MIL and by setting the P0700 code.
P0700 means that a code has been set in the Transmission/Transaxle Controller.
This code is for information ONLY.
If P0700 is present, check for Transmission/Transaxle codes.