well if the wires are fried .. thats a good place to start some rewiring...

What are the chances it is the computer too?

Have these "mechanics" been putting in new parts like the starter and battery since your car died? When your car quit, would it turn over and just not fire up? Or was it just absolutely dead? If it's not getting spark, I would assume that it turns over? Have any of these guys bothered to check to see if the timing belt broke? All they have to do is remove a few bolts on the timing cover and see if the belt is frayed or broken.

I dont know if they have checked that- will ask him to check tomorrow. Yes it turns over but does not start. thank you for idea!

Did you smell anything burning when this vehicle first malfunctioned? Seems to me you should have seen some smoke if indeed something was "FRYING" I'm having some problems with this narrative. Suggest when you have this issue resolved....ask for ALL the old parts which were replaced...including ...what ever fried. Good Luck