There are multiple ways to automatically back up photos, Google themselves will do it so I would check your Google account as chanchan05 suggested.
If the phone has been connected to the computer before it might work, but by default these phones are set up to prevent data being read and taken off by a comouter, usually need to toggle a setting on after plugging in. Its worth a shot but odds are nothing will happen.
There's also an SD Card slot, did you have one in the phone? If one was in it should have been saving the photos to that, in which case you just pull that out and put it into another phone, tablet, or computer.