rough engine at very low speed

I have 98 Windstar with 175K miles. It idles fine, and runs fine except one problem. When I push the gas pedal lightly to go, the engine gets very rough (almost about to die). If I push the pedal slightly more, engine smoothes out immediately and runs fine. I tried one of fuel cleaners and it had no effect. Any thoughts?

First thing I can think of is to have the IAC (Idle Air Control) Valve cleaned!

First thing would be to make sure that you are up on routine maintenance, fuel filter, air filter, spark plugs/wires.
A can of Berryman's B-12 Chemtool in the gas tank to clean the injectors.
A good inspection of the vaccum lines to make sure that you don't have a vaccum leak.

Is the battery in good shape?

As mentioned, cleaning the Idle Air Control valve (IAC) with WD-40 or SeaFoam 'Deep Creep'
Remove the IAC.....hold it so that you can spray into it....and have the fluid run out.....rinsing out dirt/crud, leaving a lubricating film.

The above is all good to go over before winter sets in.

A good inspection of the IMRC system (3.8L engine only), the 1998 still uses vaccum driven actuators to pull the IMRC to the CLOSED position.
If 1 or more of the IMR shafts is not closed fully, it can cause low RPM issues.
Springs pull the IMR shafts OPEN when there is no vaccum (like when the engine is not running) and vaccum pulls the IMR shaft to the closed position when you start the engine.
The PCM controls the IMRC vaccum solenoid to have them open/closed.

With no CEL, these are the things that I would check out first.

Checking the fuel and air filter is a very good idea.
It happens also when you accelerate on neutral? Or only when you're driving?

As suggested, I cleaned IAC but no effect. Since the problem is very reproducible, I pulled vacuum lines one at a time (whatever I could find). By luck, when I pull out the vacuum line on the top of EGR (I think it is a vacuum line) and the problem disappeared. At least I can say the problem is the EGR system… I’ll try to take it out and clean it as many of you have done. Will let you know if I succeed. BTW, the roughness happens while in neutral as well.

An update..
I took out the EGR and it looked ok.. no blockage and the valve seemed to open and close ok. I cleaned it anyway and put it back… still the same problem. The next one was the pressure sensor sitting right next to EGR (I believe this controls the EGR??). It is replaced but did NOT fix the problem. Put the old one back after cleaning the two tube holes.

I was about to give up but I remembered reading about cleaning the small holes in the in the intake manifold, which tend to get clogged up. I un-tightened 12 screws, lifted up the cover just enough and indeed the four holes near EGR side were clogged up. I tried to take the cover out, but something was holding it in the back side. I lifted up the cover some more such that I could put my hand in and unclog the holes. I used a long screw with a sharp end with a long string tied in case it falls into a big hole… With the unclogging, the problem is gone. It took about five hours for the whole operation. It was not particularly difficult.

SamNovice,

So did cleaning out these holes resolve the issue, or does the problem still exist?

TIA,