merely having power to the screen does not indicate whether this would be software or hardware cause, however in the majority of iPhone issues it is indeed software so let's hope that is the case here.
Sadly, though, the issue you are having likely means the software itself has "crashed" on the device.
First, let’s attempt resolving this issue with your Apple device by trying a hard reset, then proceed from there if that does not resolve the problem:
Disconnect the device from it's cord, if plugged in.
Press and hold your Sleep/Wake button (on the top) and Home button (on the front) together for around 10 seconds.
When the Apple logo appears, release both buttons.
The next thing you should see after the Apple logo is the home screen a few minutes later.
If the above does not work, plug it straight into a power outlet and try again.
If it still does not work, then I'm sad to say that anything that was on the device is already lost and will not be retrievable. However, if you regular sync with iTunes or have iCloud turned on in the iPhone then you likely have a back up of at least part of your photos already.
Make sure you have downloaded and installed the latest version of iTunes on your computer before attempting this:
(Mac users can run System Preferences > Software Update (or “Apple Store” for OS X 10.9 users) > Check now to get the latest version for their system in most cases.)
Disconnect all cables from your Apple device.
Open iTunes on the computer
Turn off the device (press the sleep/wake button on the top until the device completely shuts off.
Press and hold the Home button. While holding the Home button, connect your device to the computer running iTunes. (If your device doesn't turn on automatically, turn it on.)
Continue holding the Home button until you see the Connect to iTunes screen.
iTunes will alert you that it has detected a device in recovery mode. Click OK, then restore the device.
It will ask whether you wish to restore a backup from iTunes or from iCloud. You should use which ever has the latest backup of your personal data.
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Thanks and good luck,