So you have verified there is no spark when it is cold?

Do you smell gas when you crank it in the no start condition?

I know it sounds too obvious....esp since she cranks..I had same problem with non-p car.. tried everything, when all else failed, got a new starter... Fixed problem. Can't explain? Something to ponder?

Double check signal at switch. It sounds like a switch problem, sugegested above:

At "run" position, you should have power on the run wire to DME. When the switch is moved to "Start" the signal is not there.

I seem to recall a post many years ago regarding a fuse or something having to do with lights or something that was tied in to a no-start issue.

Also try a little starter fluid when cranking. If it does fire up briefly, you will know it is fuel related.

This post copied from an old post may help:
1 coil ground (1)
2 micro switch (throttle, idle), closure to ground at idle position
3 micro switch (throttle, wot + throttle valve) test connection b, closure to ground at wot
4 t54, starter active, +12 volts while cranking engine
5 gnd
6 gnd, air flow sensor, ntc I
7 air flow sensor +
8 speed sensor +
0.6 to 1.6 kohms between pins 8 and 27
9 air flow sensor -
10 plug for exhaust data (ground)
11 t54, speedo
12 test connection a
13 ntc II
1.4 to 3.6kohms at 70oF
160 to 210ohms at 212oF
14 t55, injector control signal
15 t55, injector control signal
16 gnd
17 gnd
18 +12v
19 gnd
20 control signal, dme relay
21 t54, goes to speedo
22 air flow sensor, ntc I +
23 .75ohm connection to pins 5, 25, 26, 8 & 27
24 oxygen sensor
25 ref mark sensor +
0.6 to 1.6 kohms between pins 25 and 26
26 ref mark sensor -
27 speed sensor -
28 altitude sensor
29 a/c compressor clutch ‘on’
30
31
32
33 idle speed positioner +
34 idle speed positioner -
35 +12v
pinout, looking at the DME connector, NOT the DME...

thanks for this.

and no we are still not running as yet.

If I understand correctly: You can push-start fine. You can crank and the engine turns over fine but never fires: In that case the electrical part of the starter switch could be bad. The easy test is to try a remote starter. Hook it to the starter motor relay and fire away. If it works you have identified the starter switch.

The other possibility is the DME itself. It has an input (pin 4) that looks at the starter terminal and turns the fuel pump on during cranking. The fuel pump is turned on by the DME if one of the two conditions is met:
1. Flywheel rotatation with sufficient speed (push-start or engine running) detected at the speed and reference sensor
2. +12V (cranking) detected on pin 4

I guess your starter switch is not maintaining +12V to terminal 31b (the DME) while in the START (cranking) position. As a result no spark and no fuel during cranking. When you push-start the switch is in the ON position and all is well.

If the sensors were bad the engine would never run at all. If the battery is bad cranking would be very slow and sluggish.

Ingo