Update:

The last time she got stranded she had NOT locked the car--it was just a gas up stop. So, realizing the car had never acted this way before I changed the starter, plus all the alarm stuff AND your good comment, I figure it had to be a loose connection of the small 12 volt connector for the solenoid on the starter.

Jacked it up and pulled the brown plastic connector out, cleaned the inside, closed the metal opening of the connector down a little with a small screwdriver, and reconnected it. So far so good. We shall see.

Let's hope this gets the beggar, bet these phone calls are getting rather old now! That's all else I can think it would be really, a loose connection somewhere. I suppose if this doesn't cure it it might be worth trying the connections to the trans. lockout switch too.

EDIT-: I didn't know you'd changed the starter, was it completely dead for you to change it? One more possibility is the new solenoid could be faulty though I'd doubt it, you could prove it out if it does this trick again by putting a test lamp on the signal wire that you tightened & earth. If it lights when you try to start but still no go then it's gotta be the starter, hopefully though (everything crossed this end!) cleaning & tightening this spade gets it...

Ran a new 12 ga. wire thru an inline fuse right off the battery, then to a small $5 Autozone relay on the left side under the hood. Ran it down and soldered it to the brown solenoid wire. Then hooked up a small pushbutton switch inside the car to the relay's coil.

Told wife if it failed to crank to leave the key on and hit the button. THEN if it didn't crank it was the solenoid or wire connector. Told her to wiggle the new wire and try again before she called me.

Today she stopped on the way home for 10 min., didn't lock the car. NO crank. Hit the button and drove home! This is the nuttiest problem I've had for a long time.

Sounds like that darn theft deterrent system is still giving you problems. I had a similar experience in my car as well. I disconnected the theft deterrent computer completely, cut and grounded one of the wires on the TDC harness as shown in this post:

http://www.toyota-supra.info/forums/...rm-system.html

Hard as hell to get at, but no problems since then. :D I hope this is helpful

EDIT: I followed the instructions in burton51m's post

Turns out the problem isn't the theft computer, it's the starter relay that's under the pass. side interior kick panel. It works fine when the car interior is cool, say under ~80-85 F. Above that all it does is click.

I need to find a new or good used one, for a car with an automatic trans.

Problems
 

Always a challenge when a gremlin gets in your car. Could be as simple as bad connection to the battery terminals, though not likely I am sure you already checked that.

I have wired a $5 AutoZone relay in parallel with it (separate switch), and that one works every time.

The stock silver relay box says "ECT" near the top.