My iphone keeps turning on &&: off every 5 min &&: its not letting me backup?

This morning my iphone said it had no sim card, then it started shutting on &&: off.
the guy at the phone company said to back it up so my information doesn't delete.
i'm trying to back it up but it keeps turning off.
is there another way to back up my info or how do i keep it on?"

Added (1). Uhmm so i tried keeping it off, connecting it then turning it back on like you said, it still keeps turning off.-…
&&; i tried to reboot it but it still turns off &&; DFU mode isn't helping either -.-
is there another way to keep it on?
really don't wanna lose my info, have 4, 081 pics, over 100 contacts, important txt &&: well yea.
if anyone knows any other ways can you please let me know.

Keep it off when you connect to pc.put wire in.open itunes, turn on iphone

Try a soft reboot by holding down the sleep and home buttons down at the same time until your screen goes black. If this doesn't help the problem you can try puting it in DFU mode then backing up if you don't know How to put your phone in DFU mode you can learn how very easily using YouTube tutorials

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