Sounds like a serious electrical problem. To peg all the warning lights - could be a number of things causing this. Main wiring loom is damaged or shorted somewhere, bad intergration relay (most of the car's wiring runs to this common connection point), excessive electrical noise from EMI/RFI interference, bad wiring to the ECM, etc.
History on the car - any major electrical or mechanical repair prior to this happening on the car? Was the car ever involved with flood damage (issues you are seeing are exactly like how many flood damaged cars act)?
Definitely do not reset the ECM when this happens. Given that it is an intermittent issue, hard to track this down without seeing it happen in the first place. In this "stuck" mode, they can try and query the ECM and see if they can pull any data from it.
Not understanding how you cannot rev the engine - this generation has a cable actuated throttlebody, even if the computer was oblivious to the TPS setting, opening the throttle plate will change the amount of air being sucked in. If you stand on the accelerator and the car doesn't see the change from the TPS or MAF - it will stall.
Same with the transaxle not engaging - it is electronically controlled, but only in shift strategy, solenoid operation. Even if they are not controlled by the PCM, you should be able to shift out of part and drive away in top gear (3rd). It is a failsafe in the transaxle logic, incase of the PCM cannot control the solenoid or if the solenoids fail.
Are you certain the is running at the time? If the car stalls during operation, all the warning lights will light up, as the key is still in the RUN position - stepping on the accelerator, trying to shift the transaxle, etc. when the car has stalled will act like the car is completely dead. The rest of the electricals will still work - power windows. door locks, HVAC fan settings, radio, lights, etc. - because the key is in the run position.
Tried removing the key and reinsert the key restarting the car? Tried to drive the car with just the one key, excessive weight on the ignition switch can cause it to wear out sooner, causing funny behavior - car starts and runs, but mid turn might decide to turn off (bumped the switch)?
Does the car have a factory or aftermarket alarm system? Made sure that it was fully disarmed, before starting the car? Possible the control box is damaged, causing intermittent operation - many aftermarket ones have a starter kill, can't start the car until it has been disarmed. Unplugging and replugging the battery can cause these alarm systems to default to a weird mode. Some immediately complain if the power was cut off, some get stuck in a weird operating mode and may cutoff the ignition in the middle of your drive.