Need to find my half brothers. What do I do?

[wendy c]

They are not 7 or 8 yrs old if born in 1996. but they still are minors, so there should not be public documents. And if dad isn't on the birth cert, then he may well NOT be paying child support or even aware of their location.
Your option is trying to find the mom. She might have changed her name since that time, by marriage, or moved to another state. You might TRY using google with her old name. Use "quotation marks" with the name and include Florida.
Other than that, it is correct that privacy laws are going to limit what can be done.
He may not be paying support, but dad may have further information.. IF HE IS WILLING to discuss it.