1999 Chevy Cavalier Puzzling - throttle not responsive, car

My Cavalier usually runs fine. However, at times it gets in a mode where the following occurs:
-Tranny shifts extremely hard, rattling the car.
-Tranny won't shift during normal acceleration unless I let off the throttle a bit
-The throttle has a delay of about 1-2 seconds in responsiveness
-Usually, this mode is accompanied by the "ETS off" light illuminating on the dash

The vehicle will go back to normal operation (shifting and throttling fine) after turning off the engine or letting it sit a while.

My first thought would be to replace the shift solenoid, but would that explain the sluggish responsiveness of the throttle? Without a check engine light on, how am I able to further diagnose?

Thanks,
Scott