When you say 'run on a step' do you mean you're stepping on the throttle? I'm assuming you mean that you're tapping the throttle here is that right?
That's tough, could be a few things. How do the spark plugs look? That's a lot of mileage. May try pulling and cleaning the MAF. How does the air filter look? Is the intake and tubing from the MAF to throttle body in good shape?
Does the car smell of fuel like it's running rich?
At what RPM does the engine idle? Should be about 700-800 RPM.
How long since the coolant has been changed/flushed? It's a really long shot but, if it's REALLY really old I've seen coolant actually conduct small voltage which throws all of your sensors out of wack. Here's how to check for that as an issue. I wouldn't freak out if it comes to this; you don't need to replace everything just flush the coolant and I would replace the coolant temp sensor in this case as well, they're not expensive and absolutely vital as an input to your engine's fueling and warmup enrichment tables.(make sure it's the CTS and not the sending unit for the dash. The CTS has 2 wires, sending unit only has 1)
https://www.familyhandyman.com/project/ ... ultimeter/
We can do a few checks to see if something has gone bad. I would check and adjust the TPS. Thats fairly easy. Its a long shot but check the ECU for codes. This is separate from OBD2 (which your car may have if it's late model 96).
How to check codes on S13/S14 ECU