Can a professor not pay a student who will be working on a funded research grant project?
That would be illegal in the US. That doesn't mean it doesn't happen, but here, all people who work are entitled by federal law to be paid, at least, minimum wage. If he refuses to pay you, you can either quit, refuse to do the work, or call your state's department of labor (or whatever it's called) or the US Departmen of Labor. I don't think Florida has such a state-level department. 

If all the money that came from the grant to your school was swallowed by the department, then they should pay you instead. In the US, awards by the NSF are made directly to the university with the requirement that the funding listed in the budget for the workers must go to the named PI and the other named people or (often) unnamed student who will do the work. There are other line items that go to the university (indirect costs, etc.), but I'm not considering those here. The university, essentially, must send the salary money down. I don't know where you are or what terms the granting body puts in its terms, but some similar model seems likely.