When you say "broke" what does you mean? Someone might be able to give you advice about fixing it.

You should probably work out a plan for telling your school, explaining things you could do to replace the laptop and also why you do not want your father involved.

Get help with the wording of the letter.

I'd like to think that teachers would see this as a sign of maturity and would work with you (clearly a non-malicious person) to repair or replace the laptop, but perhaps I am ridiculously optimistic.