Okay, this is gonna be a long post. I have a 92 Integra LS. The idle is surging from about 500 to 1100, it's not always that low or high, I think it varies based on the temperature of the engine and how hard I am driving it. It is always a steady surge of at least 300 RPM though. It does this all the time, regardless of engine temperature or if I am pressing on the gas.
I am not an extremely knowledgeable car person, but I have been dealing with this problem for 6~ months so I have learned a lot about it, but I still get names and things wrong so feel free to ask questions if you are unsure of the accuracy of anything I have said.

Here is a list of things I have done to try to fix it.
-Replaced the Idle Air Control Valve, replaced it 3 times, cleaned the screens on ICAV's and area on the back of the throttle body where it connects.
-Fast Idle Valve, tried cleaning it twice and then replaced it.
-Also with both the IACV and the FITV I took the air hose off the front of the throttle body to access the two holes that come from IACV and the FITV. Plugging the FITV after the car warms up makes no impact on the surge, it still does it without any change in fluctuations. Plugging the IACV causes the car to die immediately if its completely up to temperature. If I crack the throttle plate just a little bit, enough to keep the car running and then plug the IACV hole it still surges.
-Intake Air Temperature Sensor replaced with a new one.
-Coolant Temperature Sensor replaced with a new one.
-MAP Sensor, these were around $250 for a new one so I got some from a local junk yard and swapped out 3 different ones, made no impact on the surge.
-Oxygen Sensor, had a local mechanic swap this with one he had, it was reading within specification on both and appeared to be working correctly so he put the original one back on.
-Had same mechanic smoke test the system for vacuum leaks, found none. Also used carb cleaner on vacuum/air lines and found nothing.
-PCV Valve swapped with a new one. When I changed this the old one still had a rattle to it when I shook it so it was probably fine.

When this problem first started I had some CEL codes, they were 3, 5, 6, 7 and 10. These are most of the sensors listed above and after they were swapped the codes stopped showing.

Possible related/unrelated issue(s).
-When the car is cold it stutters a lot on starting it. It runs very poorly with the RPM jumping from 400~ to 1000~ and will continue doing this for a minute or so until it warms up a little. However if I give it gas it immediately drops RPM for a second and then spikes up and the rough idle goes away after a few seconds of holding the accelerator.

-Recently I had a dead battery and replaced it without doing any checks, it was a 10 year old battery anyways. About two weeks later I got CEL, never checked it and the next day my battery was dead again. I tried to bump/push start the car, (its a manual, if you pop the clutch while the car is rolling it starts the car. Was a nifty trick my room mate told me that I didn't know.) When we did this the car started but was running very badly, there was very little power from the engine and half of the electrical functions of the car didn't work very well at all. We were able to jump the car with cables and it worked just fine. I was told that most of the time this is caused by a bad alternator. Already bought an Alternator, going to change it out this weekend.

Any idea's or things to check or recheck would be greatly appreciated.
This is a short 1 min video of the Idle surge looking at the engine.

 

Did you ever figure out the issue you were having? It sounds like the exact same issue I'm having now... I've also tried what you have tried.

 

Have you tied bleeding the air out of your radiator's coolant?

Try one of these...https://www.amazon.com/Lisle-24680-Spill-Free-Funnel/dp/B00A6AS6LY?th=1

 

NOTE:
Guys! This post is from 10 years ago. He is probably no longer around, he probably doesn't even have the car anymore.


Most of the time, its one of these two. Usually the FIV in my experience. Especially if a car has sat for awhile.

Video is private, I'm unable to view it.

Have you done an Idle relearn procedure? I had something similar, where the last thing on Honda's list to check, was under the fuse box, and I would have to pull and possibly replace the fuse box. I did the idle relearn for the computer. and it actually fixed my problem. Also, in my experience, if any one has messed with the adjustment on the throttle position sensor. In my opinion, they ruined the throttle body. Those are factory set, I've never had to adjust one that was factory set. Once people mess with them, it never ever seems to be able to be set correctly afterwards.

Do you have a FSM for your car? there is a section that talks about idle issues, the last one being some sort of electrical load, raising the idle and lowering it. I think its electric load for headlights, AC / Radiator Fan. I believe its mounted to the underside of the fuse box. But that's been at least 10 years ago when I looked into that problem. Since you've stated that you have had battery and alternator issues. Maybe that has actually gone out. I've never had one go out in the many many Honda's I've worked on. But these cars are now quite old by car standards.