How do I retrieve data from an unresponsive iPhone?

Mus57er wrote:

old phone screen totally froze and hard reset does not work. apple told me it is helpless to get data back, and provided a new phone under insurance. there has to be a way to get back the pictures and everything. phone still is on, but does not work.

If the phone does not work, there is no way to "get back the pictures and everything" from the phone itself. From what you are telling us, Apple themselves also think that data recovery is not possible.

it is my fiancé’s phone and she is very concerned about all her phone numbers, and pictures, apps etc. apple said that they would be able to transfer items that are backed up though the Apple ID, but most of, if not all of her photos are not.

If she was using iCloud Photos, any photos that made it to iCloud would be available from iCloud – and could be seen by logging into https://www.icloud.com/ . (With photos in a backup, you would need to restore the backup, wiping the contents of the target phone, to see what was in the backup.)

From what you're telling us, it sounds like "most of … her photos" were not backed up in any way, in which case, those photos are gone.

there has to be a way to get back the pictures and everything. phone still is on, but does not work.

Sorry, there is no way to get at the data on the phone.

apple said that they would be able to transfer items that are backed up though the Apple ID, but most of, if not all of her photos are not.

The technician will be able to transfer data that was backed up, but they cannot transfer data that was not backed up.

since the phone still technically is on, my thoughts are that there has got to be someone out there who can take the old phone and transfer the data onto the new one without physically operating the phone

I'm sorry, but your thoughts are incorrect. Up to you if you want to believe any of the wild claims that you might see on the Internet, but don't give them a dime unless and until they transfer the data that you want.

The photos are usually either in the iCloud backup, or the photos are in iCloud Photos and available when using the same Apple Account. If the photos are in neither place, then they’re gone.

Recovery services will usually expect payment before performing services, and may or may not retrieve any data.