Do an ohm test on your CPS. Mine did almost the same thing, I thought it was an unplugged vacuum line to the MAP also.
It turned out to be that my CPS was right at the edge of the allowable ohm tolerance. If I remember correctly it tested at a round 292 ohms or so (supposed to be 200 +/- 75 if my memory is correct, better to look it up again to make sure). The CPS got really temperture sensitive, it would start at one ambient temperature and not another.
It could be something else, but it sure sounds familiar. You may also want to test your CPS wiring and connectors, between the CPS plug at the motor and the ECU, if you can't seem to find the problem. I had some resistance in the connectors, it all adds up.
Might also be a sticky IAC, if the air fuel mix is screwed up, it will hardly idle, you have to find exactly the right spot with the throttle (usually between 1/8 and 1/4). Usually if you do manage ot get it atarted, it will die as soon as you release the throttle.
Really weak spark can also cause something similiar. Thy cylinders flood and it will try to ignite, but doesn't quit make it.
It will idle really bad and stall if the EGR is stuck open.