Hi BB-
"Any help" is my middle name.
1. What was done to the car between the time it started yesterday and this morning? Some change to or disconnected electricals could be causing the problem. Push the guys who are working on it by finding out exactly what they were working on betw. the time it started and would not.
2. Check battery charge with voltmeter...Did it keep the charge from the beginning of the week? If so, check its cables, fuses, grounds for condition and be sure they are hooked up where they should be...don't forget that ground from the "-" batt cable to the inner fender.
3. Take the alarm/ign cut-off out of the equation...Do you have a way to disconnect it/defuse it? Ditto for the radio and antenna.
4. Check starter solenoid...I used to have a starter with a balky/sticking solenoid and had the same symptom you describe...it was intermittent and would unstick with a few sharp mallet whacks.
5. Check starter for oil saturation...esp if there is a rear main leak.
Hopefully, someone with more electrical experience will chime in with info about other grounds and circuits I have not mentioned.
Good Luck!
Please let us know how you progress.
Steve