You described everything that happened to my 96 accord.
The transmission if fk up lol. You will need a new transmission period.
$1200 is extremely cheap. What happen is when u drive the car for a little bit the transmission get hot or something like it and it just quit, the engine will rev normal but it just won't go anywhere. The exact, I mean exact same thing happen to me. Once u replaced the transmission the engine check light will go away (make sure they change both solenoid even if they are good).