Codes P0740, P0753, P0758, P0785, P2761 and P2101, Transmission?

With all of these code I would clear them, then turn the key on without starting the engine and re-run the cdoes, we are looking for the most prevalent code, if no codes come up start the engine then shut it off and run the codes again. Here is more information:

The codes you provided are diagnostic trouble codes (DTCs) specific to your 2005 GMC Envoy. These codes are related to the transmission and engine control systems, indicating potential issues with various components. Here's what each code refers to:

P0740: Torque Converter Clutch Solenoid Circuit

This code suggests a problem with the torque converter clutch solenoid circuit. The torque converter clutch is used to lock the torque converter in certain situations to improve fuel efficiency. A malfunctioning solenoid or circuit can lead to poor transmission performance and fuel economy.

P0753: Shift Solenoid A Electrical

This code indicates an issue with shift solenoid A electrical circuit. Shift solenoids control the shifting of gears in the transmission. A malfunction in the solenoid or its circuit can lead to improper shifting or transmission issues.

P0758: Shift Solenoid B Electrical

Similar to P0753, this code points to an issue with shift solenoid B electrical circuit, which controls a different shift in the transmission.

P0785: Shift/Timing Solenoid

This code suggests a problem with the shift or timing solenoid circuit. The solenoid is responsible for controlling the timing of gear shifts in the transmission. A malfunction can lead to shifting problems.

P2761: Torque Converter Clutch Pressure Control Solenoid Control Circuit/Open

This code points to a problem with the control circuit of the torque converter clutch pressure control solenoid. This solenoid helps control the operation of the torque converter clutch, which can affect transmission engagement and efficiency.

P2101: Throttle Actuator Control Motor Circuit Range/Performance

This code is related to the throttle actuator control motor circuit. The throttle actuator controls the opening and closing of the throttle plate in the engine's intake system. A malfunction can affect engine performance and response.
These codes collectively suggest potential issues with your vehicle's transmission, torque converter, and throttle control systems.

Also, is the transmission fluid burnt?

Yes, it sounds more like the harness is bad I would check the main wiring connector at the transmission and the wiring in general for damage/corrosion. Also, it could be a bad PCM.