88 Integra starting problems (cranks and cranks)

This problem is similar to a post of a few months ago, but not quite.
Here are the details. 88 Integra RS, 120k. Recent air filter. Plugs not new but okay. Could probably stand a cap and rotor. It has great
difficulty getting started. This problem has been getting steadily worse over the last year or so. It used to be only a problem on hot days when the car was already warm. Crank, crank, crank, and nothing. Often, just shutting off the ignition and letting it sit a few seconds, then retrying would be enough for it to start right up. Now, that does not even help. Once in a while the car will actually start right up with no problems But this is rare now and pretty much only happens after sitting overnight. It's at the point now that all the cranking required to get it started is nearly enough to run down the battery. IOW, it's not very driveable now.
I've tried all manner of oddball things to try to help it out, from holding the gas pedal all the way to the floor while cranking to pumping the gas, to keeping off the gas completely. Nothing seems to make any difference. When the car finally does start, it's definitely as though only one cylinder is firing for a few seconds. It will chug, chug, chug, and I often need to keep the starter running until it gets chugging quickly enough to run on its own. Then, all of a sudden it's as though all the cylinders kick in at once, and it's up and running, very nicely.
There is never any black smoke once it starts. If anything, I'd say it's not getting enough fuel upon startup. If this were a carbureted car, I'd say without a doubt that the accelerator pump is not functioning propery, and it's just too lean. This can also be evident when driving and taking off at a green light, because sometimes the car bogs and nearly dies for an instant, which is another sympton very reminscent of a bad accelerator pump (if it were carbureted). Otherwise, the car runs reasonably well and smooth once it's running.
I poked around the intake manifold and such, not sure what to look for. I did notice a little tang that appears to control the idle speed looked bent out of whack and was not making any contact with the throttle lever. I tweaked it so that the car now idles around 1000rpm in neutral. It used to be about 600 which was just too low. None of this helped the starting problem in any way though.
What could the problem be? Is there something similar to an accelerator pump in EFI engines? If so, that's the first place I'd want to look. If not, what else might be the trouble? Is there some way I can diagnose this better?
Thanks.
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The part about "It used to be only a problem on hot days when the car was already warm" got my attention. See http://tegger.com/hondafaq/startproblems.html#mainrelay - that is basically the fuel pump relay. It is a very common problem... maybe universal if a Honda gets old enough.
Mike
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I agree on the main relay. 1000 rpm is too high for idle on a warned up engine,600 rpm is about right.
--
Jim Yanik
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Correct idle (full-hot, EACV connected) is 750rpm in neutral, automatic or manual.
If the idle speed is to be adjusted, the EACV must be unplugged prior to turning the idle screw. Idle with EACV disconnected is 650rpm.
--
Tegger

The Unofficial Honda/Acura FAQ
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