1994 300zx idles and turnsoff when quickly accelerated

[FairZ]

When I turn on my z it idles and then when I accelerate the car it squeals and then turnsoff I then restart the car and turn it off but when I turn it off and take the key out of the ignition the car stays on , someone please help

[DCaff300ZX]

Welcome!
BTW, listing the year and whether NA or twin turbo in your personal info, to be listed with your name and other info (you list "Nissan 300ZX"), is a great help with diagnosis as there are major differences between the various year cars, and convertibles as well.
Wow, this sounds impossible but I give you the benefit of the doubt. Only thing I can say is there is obviously something VERY f-ed up with your ignition switch if this can happen, and is where to start looking.
Try looking for tests in the online service manual that you can download from the "everything you need to know about the Z32" sticky at the top of the page, and Good Luck with that amazing problem!
Oh, and let us know what the problem was when/if you are able to fix it.