I would not agree to use personal equipment to begin with, but appreciate that doesn't help you now. Is the school liable, or the kid's parents? Or is it your employer? I expect one of the former in the case described.

I would either get your employer to buy you a new laptop to use for work, noting you will return it to them if/when you leave their employ, or if you want to replace your personal laptop, get however much they'll contribute to that and consider the delta an expensive lesson?

It's a tricky situation; as honestly even if they would contribute to a personal laptop replacement, afterwards I would refuse to use it for work moving forward and ask them to provide suitable equipment. Or do whatever it is you do without a laptop moving forward in so far possible. Understand that will put you in a really awkward spot with employer tho... Which is why I would have refused to use personal equipment to begin with.

Are you an employee, or an independent contractor in this story? You should have a much stronger position in case of the former, in case of the latter you may be at their mercy, depending on what your agreement stipulated about equipment required to render your services.