iPhone 4 water dmg shows apple logo and then reboots

I'm helping a friend try to recover some data from her iPhone 4. She told me it was water damaged. She says she tried the bag of rice routine to dry it out and then tried rebooting it. She took it to an iPhone repair shop (not an Apple store). After a couple of days, they said they couldn't get it to boot either.

Her concern is that she does not have a current backup, and there are family photos that she wants to save.

I do data recovery and digital forensics on computers and cell phones in general, so she asked if I could help. But, I admit, I'm not an expert at iPhone repair. But I'm learning fast through this site.

I've been reading through here for the past few days and have gone through the water damage repair guide. I have disassembled the phone and gave it a good cleaning as instructed.

Here are the symptoms.

Only when connected to the AC charger or a PC, will the phone power up. It will show the apple logo for several seconds, and then it will go blank and repeat. It never gets past the apple logo.

I can force it into recovery mode, and iTunes will recognize it only in recovery mode; but iTunes wants to do a restore before doing anything else. I don't want to risk losing any data on the phone, so I have not attempted a restore. I use Oxygen Forensics software in my work, so I attempted that route. It will recognize the model of phone, but will not communicate with it for data transfers.

I am able to communicate with the phone using iRecovery to take it out of recovery mode. Also, the error message I see when using iRecovery states that there is low current.

I replaced the battery, but no change in the symptoms. I have not yet tried changing out the docking port and was wondering if I should try that next before ordering one.

I'm hopeful that the phone may live, since I can talk to it through iRecovery while in recovery mode. I'm assuming that means the logic board may be ok, but I'm hoping someone here with more knowledge could help answer that. If it seems the logic board may be ok, then I will continue trying everything I can to get the data.

Thank you very much for any assistance.