1992 Lincoln Town Car Acceleration issues. Like nothing iv

1992 Lincoln Town Car V8 Automatic 93000 miles

i bought this car a few months ago with my dad there so he was able to check it out. It ran perfect. Nothing but cosmetic stuff needed to be done. I was unable to drive it for a few months and so it sat. Now when I began driving it a few weeks ago, it continually does this weird acceleration thing. Well, it ONLY accelerates if you barely have your foot on the gas you have to EASE it up to whatever speed you need to get to because if you put your foot harder on the gas, it feels as if you just hit the brakes hard and just refuses to accelerate. It kinda just feels like its in neutral if you try to accelerate too much. No crazy noises, and it doesnt ever stall. My dad thought maybe it was the fuel filter and so did our neighbor (who buys crappy cars just to fix for something to do!) So we replaced that and it still does it. We ran it out of gas and put fresh gas in. Nothing changed. I can drive it, but it takes forever to get up to 35! The weirdest thing is that the check engine light goes OFF when its not accelerating. Its ON when its catching speed. (We JUST recently were able to find the diagnostic connector for this car--under the hood, and had a part ordered because it was so eroded. So we arent sure why the light is on yet)