I'm Lucy, and I'd be happy to answer your questions today.
Florida Stat., Section 83.67 lists some examples of utilities, but it also says that it's not a complete list. If the lease says that the landlord is providing cable, internet, and telephone as part of the lease, it's going to be classified as a utility and he cannot shut it off without going to court to evict you. Also note that Florida Statutes, Chapter 366, which governs public utilities, talks about cable television.
You can go back to court and file the forms to ask that it be turned back on today. How long it'll actually take depends on how busy the courts are. It is unfortunately not likely that you'll get a court date before August 25. However, if you have to pay to get your own service installed because he turned it off, those are part of the damages you can request. He has to pay your actual damages or three months rent, whichever is more. He can also be required to pay your attorney's fees if you choose to hire a lawyer.
Because the lease requires the landlord to provide your cable, the judge can require him to turn it back on even if it's not considered a utility, because he's still in breach of the lease. He could order you a partial refund of rent for each day you had to go without (which will be deducted from the August rent you owe). But the law is on your side no matter how "utility" is interpreted.
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