My nephew spilled a large cup of water on my laptop and I think its worthless now. Will my brothers home owners insurance pay for this?
The laptop is worth atleast $1600 so no $600 wont cover it.

Probably. But you may not like the results of filing a claim.

Many homeowners policies have a $1000 deductible and filing a claim is often grounds for policy cancellation or a huge premium increase. You can buy a new laptop for $600, which is probably less than the deductible. Work something out with your sibling (forgive your nephew, ask your sibling to pay, etc).