That are the codes that come up when there is a problem with the transmission control module Code P0700 = Trans control malfunction. Code Uo404 = Invalid data received from control module gear shift. This means Trans Control Sys malfunctioned. I have a '06 G/C w/ 124K miles on it and get the code occasionally, and it always resets itself. There are a number of posts here that deal with this ...
I ran the code at advanced auto nearby and it showed p0750 Shift Solenoid A malfunction and a generic transmission p0700 code, with the additional battery loss history from me trying to reset the ecu.
It has P0700 (Transmission Control System Malfunction) and P0657 (Actuator Supply Voltage A ckt/open) codes. Reverse works fine, when it is in drive it is stuck in 1st or 2nd gear.
I've had several codes for AT on 05 jeep GC 5.7L: p0073, p0700, p1684, p2706, p0934. The weird thing is, after clearing the codes and rerunning the car, I got same codes back except for p0934 (AT pressure line sensor).
The P0700 is a generic code signalling something from the tranny has triggered the MIL lamp to illuminate, as you say, but the series of P0730's that were most recently pulled ARE NOT generic codes and specifically deal with a mis-match between input and output shaft speeds. Further, the codes indicate problems with 1st, 2nd, 3rd, and 4th gear.
The P0700 is simply the generic trouble code indicating the TCM has stored a fault. It could be the shifter bezel, line pressures, slow engagement, incorrect ratios, etc., etc., etc. Anything wrong with the transmission will throw a P0700, and you'll need to take it to a place with a much better scan tool to pull it. I would start by checking to make sure the transmission fluid is at the ...