If the school failed to make a note of the serial numbers on the laptops and you didn't make a note on the day they were first handed out, then what's to stop one of her classmates (whose parents, like you, resent having to pay for repairs) from doing a "switcheroo", when your daughter wasn't looking?
Rest assured the school will have a master list of serial numbers somewhere (minus who was issued which one), probably at the insistence of the insurance companies.
I acknowledge this in no way answers the question but it's just something to mull over while you wait. I have never encountered a computer which requested ctrl-alt-delete straight after power-up, so I will be keen to see the solution to this one for myself.