Is it legal to shut down an elevator for 3 weeks?

This isn't the kind of problem that you can deal with easily, especially in court, because it's a short term problem.  The court system doesn't often move fast enough for this.

That short term is, of course, a very long three weeks for people that end up being basically trapped in their homes because of this.

You should be able to find a listing for the Florida State Department of Elder Affairs in your telephone book, they may have a local office nearby, or a complaint or information line, and you can also go to their website, to see what practical help they can give you.