When I turn the car over, the crank is very slow in the beginning, and then it does eventually turn over, but it sounds like the car battery is dead. Also, when I accelerate hard, the car stutters as if the fuel is getting blocked, or the plugs are misfiring. The horn doesn't work at all.
It seems you have three issues. If the engine is cranking slowly, the battery, the starter, the alternator, and the wiring will all need to be checked. The battery is the most likely problem, especially since your Infiniti is more than four years old. Another possibility for a long, or extended crank would be faulty camshaft position sensor; this is a common cause and should definitely be checked. A faulty camshaft position sensor may also be the cause for the engine stutter under hard acceleration; the spark plugs should be checked as well.
As far as your horn issue goes, the horn itself should be inspected, but other parts, such as the fuses, switch, and wiring, could be to blame as well. I suggest having a certified technician, such as one from YourMechanic, come out to your home or office to run a [diagnostic inspection of your starting issue](https://www.yourmechanic.com/services/car-is-hard-to-start-inspection], and repair your broken horn.
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