iPhone 4 water damage - how to recover data?

Yes - programs like PhoneView can often read files from a device that iTunes insists must be restored. The iTunes function is to sync and clearly the OS is now in a state where it can't run itself or be updated, so the "correct" thing for iTunes is to ask for a restore.

I wouldn't say that you are guaranteed to get the photos back, but it's good you have the computer where the device normally syncs as that will have the encryption keys to unlock the storage if the device has data protection enabled.

You could also seek a quote from the usual data recovery services like: - http://www.drivesaversdatarecovery.com - http://www.krollontrack.com

You should expect to spend hundreds of dollars if you send the device in for recovery and you may have to pay if they recover anything - even one partial file - so be sure you understand what is being quoted before agreeing to a recovery attempt.

Do you have a backup of the phone on your computer? If there's no backup, the photos are not in iCloud nor synced with another device/computer, & the photos have been deleted from your phone, you would appear to be out of options.

If you are a windows 8 user and you have already authorised your computer, then definitely you can see the images on phone by Photos app in windows 8.

• It syncs all the images
• You can also try logging to iCloud.com and try your luck there.
• You can try making a new backup via iTunes to your phone and check whether you got your photos or not.

I can't be sure if this will be any better than the methods you've tried, but you could see if something like 'Phone Disk' (see https://www.macroplant.com/phonedisk/) would work for you. Unfortunately this one seems to have been discontinued now, but the company has a more recent product that apparently does the same thing. Basically it mounts your iPhone as a disk, so you can see what's on it.