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So let me get this straight, you just download the installation files and your system "shuts off". What do you mean by shutting off? This is not something Firefox is going to do by itself so it's time for you to dig in further.
What kind of system are we talking about? Tower, desktop, laptop, etc.? Make, model CPU type and amount of installed RAM.
We can take it from there. It sounds like a software conflict or some already installed adware/malware/virus but that's complete speculation.
We probably should rule out the hardware side first.