Electrical Problem on 1992 Dodge Dakota

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Whenever it gets cold the car fails to start; she'll turn over but will never catch. However, if the key is left in the run position for some time the auto off relay and fuel pump relay begin to click. After a few more minutes they stop clicking and the car starts.

I have tried to hunt for the "infamous splice 115" and have replaced as many splices as I could find.
I have also replaced the spark plugs, spark plug wires, distributor cap, checked the fuel pump, replaced the fuel filter, and cleaned the throttle body.

The only thing I can think of to do next is replace the ECM. Is there any way of checking the ECM or is there a good way of checking for bad splices that I couldn't find.

In response to lawrenceg's answer: I've determined that the engine is not getting fuel or sparking. Which leads me to the computer conclusion.

Do you know of anywhere I can get the proper readout for the computer so I can test it?
(1) Answer
Have you been able to determine what is missing when the engine wont start? Is it not getting fuel pressure, fuel delivery, ignition spark?
There are places that may be able to check the ECU if you send it to them, otherwise you need to get the information that shows what the input and output signal readings should be, then check them with the appropriate testing device, normally a volt meter.
A splice could be checked with an ohmeter, but it's best to perform a voltage drop test across the splice. Check youtube for a video on how to check for a voltage drop.
Hope that helps!