[ImperialCrown]

Let's start with a diagnosis. In order to determine what is failing, we need to make it fail for us and catch it in the act. If the weather won't produce the conditions that we need for the failure, we can try to mimic the conditions.
I did think about water turning into ice in the fuel system and preventing a start, but if there was that much water in the fuel you would likely have poor driveability in all temperature conditions. Yet you say it runs flawlessly once warmed.
Can you hear the fuel pump 'hum' in the back for a second after you roll the key on when it is cold? There is no fuel rail test port on the 3.0L for a quick fuel pressure test. It would have to be 'tee-d' into the high pressure hose into the fuel rail with a tool similar to this:
2008-11-01_133114_fuel_pressure_test_without_test_port_requires_inline_adapter.jpg
If it starts or fires after a shot of carb/throttle body cleaner spray into the throttle body air intake, then there may be a fuel supply problem.
Does the 'check engine' light come on when you roll the key to the ignition position and are there any fault codes? Does it still light below freezing?
http://www.allpar.com/fix/80s-codes.html
I almost think that it could be the PCM failing cold. It is rare, but it does happen. A PCM can be removed and placed in a home freezer for an hour or so and then put back in the car for a test start. You could do this test twice to better verify that this is or isn't the problem.
Other electrical components can fail cold. Some can set fault codes and some can't. A can of freeze spray from Radio Shack (or other store) can cool small things like sensors and ignition coil, etc. for test starts.

 

[Bob Lincoln]

You said the ignition rotor and cap are 2 years old, but how many miles on them? With my 4-cylinder, the rotor is charred after 15K miles. I had a sudden no-start from this in cold weather.

 

[valiant67]

I've had the coolant temp sensor (the one for the computer, not the sender for the gauge) fail (without an error code) which made starting in cold weather difficult and sometimes impossible. Once the weather warmed up it was fine.

 

[ImperialCrown]

The temp sensor for the PCM coolant sensor should be Bk/Rd wire? The one for the dash gauge is a Violet wire. The sensor can open at a certain low temperature. Drain some coolant before removing it and it can also be placed in your freezer for a couple of hours before measuring it with an ohmmeter. The resistance should ramp evenly as it gradually warms (no sharp changes).
The ignition secondary components must also be in good condition and OEM parts are always best.

 

[Canadianguy]

I've had the coolant temp sensor (the one for the computer, not the sender for the gauge) fail (without an error code) which made starting in cold weather difficult and sometimes impossible. Once the weather warmed up it was fine.

I had the same problem with a 3.0 in a 1991 Plymouth Voyager and replacing the coolant temp. sensor solved the problem. No error codes ever showed either.

 

[george w]

I'd say Imperial Crown's idea of a quick shot of starting fluid would tend to narrow things down to a fuel or ignition issue pretty quickly. Another quick test would be to try unplugging-replugging the fuel pump and ignition relays in the fuse block under the hood. Maybe the relay terminal contacts could be oxidized enough to cause an issue. Next would be to swap the relays around. there are several in there with the same part number. Check the connector plug on the ignition coil and the connector plug on the distributor too.
These 3.0's have an optical distributor pickup system that seems to be very reliable, but one never knows.Cap and rotor life is also very good on these engines, but it doesn't hurt to add these to the check list but they're not likely to be the cause of a cold no start problem when the engine runs flawlessly otherwise.

At least you can get the easy to check things eliminated before having to freeze the engine computer or replace the fuel pump.
You did look for computer codes, didn't you ?

 

[vanagon40]

Try one more time. Having trouble logging in and posting this evening.

I did not mean to abandon this post.

New important clue: last week would not start at 50°F in the rain.

I am still fighting the "starts everytime when I want to work on it" syndrome.

Pulled the distributor cap today and all the contacts were corroded (see below). We'll see what happens tomorrow (supposed to be cold and snow).

Thanks for all the advice.

UPDATE: 03/24/13. Car started this morning at 34°F and snow.

 

[mrneuro]

CHECK FOR CODES...

 

[vanagon40]

CHECK FOR CODES...

None (other than "55").

 

[vanagon40]

Well, back to the drawing board.

This morning was 28°F with snow and no start. Think the weather might be about the same when I get home, so maybe I can do some more checking.

BTW, I am having a very difficult time logging in and posting. I cannot log in with the Firefox browser and I.E. does not particularly like the web page. Anyone else having these problems?

 

[vanagon40]

This afternoon was 38°F with snow and no start. But I did realize that when the car won't start, the Check Engine light does not come on when the key is in the on position (the Check Gauges light also fails to turn on).

In response to another question, I do hear the fuel pump turn on, and the fuel pump appears to be working properly.

So what does it mean that the Check Engine light does not light up?

 

[ImperialCrown]

The PCM may be 1) losing its 12 volt battery, ignition or ground supplies, or 2) it is going into 'protection' in the 5 or 8 volt regulated sensor power supplies due to a short-to-ground in one of the sensors or wiring harness, or 3) there is an internal PCM failure.
No 'ck eng' light is a very good observation on your part and with a little more cold diagnosis you should have an answer.
It may very well be in the PCM itself, but you might want to follow the troubleshooting in proper order to fault the correct component.
If you can warm the PCM with a hair dryer in cold weather and the 'ck eng' light comes on and it starts up, then it sounds more like an internal PCM issue.

 

[David Eidell]

After having chupacabras, goblins, gnomes and gremlins plague my little Spirit in ways that would drive a sane person to jump, I finally disconnected every last ECU connector i could get my grubby hands on, and apply a product called DeOxit 100-D. The stuff is amazing. Gone is the psychotic gas gauge, check engine light, fan temperature erraticness. It all went away. For the first time in six years and 60,000 miles. This stuff ain't contact cleaner - it removes oxidation like nothing else I have ever used.

 

[vanagon40]

Thanks (and excuse my ignorance). Where might I find the PCM? Or the ECU?

As an aside, I had an almost identical problem with an old Subaru XT, with a defective ground to the ECU. Problem was exacerbated in cold weather.

 

[John Wood]

Your PCM should be on the driver's side inside fender. The air intake passes through it to keep it cool and you should see a wiring plug going into it. If you want to see a picture, try going to E-Bay and doing a search. You'll probably see a picture of a used one since they often go up for sale.

 

[vanagon40]

Found the PCM. No start this morning, about 32° and clear. BUT, the Check Engine light and Check Guages light both lit up with the key on. Checked for codes and found only the "55". Warmed up the PCM with a hair dryer and after about 10 minutes the car would start. Oddly, after about 5 minutes or so, the car would sputter a little, but still not start.

My plan is to pull the PCM and check the electrical connections. Probably leave it loose to heat if more effectively, if necessary.

Unfortunately, the weather forcast is for warmer weather, so I may be back to the "I can't fix it when it's not broken" syndrome.

I like David Eidell's suggestion. I too have guages that are sometimes hit and miss. The tach has always operated intermittently, but now the speedometer is erratic, and more recently the oil pressure and fuel level gauges will spike. The speedometer, oil pressure, and fuel level all eventually return to normal after a while, but the tack is always hit and miss. I always figured the problem was with the dash circuit board, and was never ambitous enough to remove the dash.

My problem now is that I have a spare vehicle I can drive and I have a lot more patience than I used to.

 

[Bob Lincoln]

Electrical connections are most likely intermittent. Clean them as best you can with a sharp tool like a dental probe, get all the grease out, spray with EFI cleaner or contact cleaner, let dry, and repack with dielectric grease. If pins are damaged, they need to be replaced or bypassed with hard wiring.

 

[ImperialCrown]

You can try to duplicate a cold PCM by putting it in the freezer for a couple of hours and then plug it into the car for a test start. (Better get the wife's permission first).

 

[vanagon40]

I don't need the wife's permission for the freezer. But I do make sure she is out of town when I put the car parts in the dishwasher.