My battery bit it saturday night, and after going through the alternator and battery tests, I replaced the battery. Immediately afterwards, the car started running like crap. Checking under the hood, I noticed the PCV valve was knocked out, so I placed it back in and that still did not take care of the problem. Long story short, I've replaced all the vacuum lines, the PCV valve, the cap, the rotor, and the car is still running rough at idle and low rpms. There is also a 10 to 15 second delay from a stop before the car will accelerate, regardless of how hard I hit the gas. The car is an 88 cougar 3.8L with 138k miles. I know the egr valve is stuck in the closed position, and am ordering one tomorrow, but I don't want to keep throwing parts at the car. Anybody have any ideas?

Auto or manual trans?

Auto transmission, AOD.

An egr valve stuck in the closed position would not cause this problem at all, however the acceleration issue could just be your trans not getting in gear properly, since its an auto it could just be slipping like a bitch.

People never put the obviously important info in.

Do you hear the engine revving up when this happens? Or is there no response?

If there is no response, then it is a fuel issue (since it must be getting air since the throttle is open). Only other possibility is spark but I don't see how.

If there is a response, but no motion from the car, transmission.

There is no response at all for several seconds. I'm going to dig out my voltmeter and pull codes on it today, see what that tells me, then pull the fuel filter and see if that's clogged. If I have any more questions I'll keep you updated.

I've never been an engine person, but

full throttle = a lot of air in your cylinders

and assuming your plugs are firing, the only other deficit can be fuel = not much fuel (probably idle levels)

Low speed + super lean mixture + full cylinder = detonation, no?

88 cougar

There's your problem.

Put a vacuum gauge on a manifold vacuum port and see how it reads when you open the throttle.
If it stays low and gradualy comes up you may have a plugged cat converter.
If the car has been missfiring for some time that can damage the cat.

There's your problem.

Try tightening up the right foot too.

Seriously though, first question I would have is; was it running right before the battery died? If so maybe something electrical was damaged in the process? Circuit overloaded? Throttle position sensor die too?