Hi Tomokotomokodesu (or simply "Tomoko"?)
I am not an expert in Japanese and I could be wrong, but from what I know I would say that the first sentence could be roughly translated as:
1) This small island "suffered from" the damage by the hurricane (could refer to a specific hurricane though imho)
> ハリケーン
の被害を受けました (THE damage of the hurricane)
2) This small island got damaged by a hurricane (we don't necessarily know which one)
> ハリケーン
で ("by hurricane" -> by some hurricane)
Hope someone will be able to confirm that !
Ed