a phone suddenly turning off/shutting down is usually not a good thing.
Plug it into a power source and it should turn back on. If ti doesnt, it might be broken.
A soft reset would most likely work but since you don't have a lock-button, you can't do that. The only other option i know of (without restoring/wiping the whole thing) is to let the battery die, then plug it into a power source.
Plug it in and leave it plugged-in. If it does not turn on within an hour, something is seriously wrong with it.
If your iPhone won't respond at all and appears dead, try this:
Connect phone to charger on computer. Open iTunes. Hold On/Off button and Home button down at the same time. After about 15 to 20 seconds, release the On/Off button and continue to hold down the Home button (sometimes up to another 30 seconds). Your phone will go into recovery mode through iTunes. Sometime you may have to try this a few times and try holding the buttons down for a longer period of time. It will work and I have had success doing this with quite a few iPhones. Once this is done you can restore from a previous backup or restore to a new phone, through iTunes.
If you are only having trouble turning you phone on and off - squeeze the top of your phone just below the on/off button and then push the button. This works well to get the phone turned on and off.
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