Read dead iPhone's files?

I have a broken iPhone 4S with iOS 8.1.1 jailbroken. It fell a lot, and the battery connector (I forgot to screw it back in) ripped out of it and the screen is broken so even if I place it and hold it with my fingers against the pins, it turns on but the screen is not possible to see as it just flickers. It also does not turn on all the way and right when it does, it just restarts so I can't connect it to my computer.

Question, how can I actually read the iPhone's HDD? Is it built in the motherboard? Is there anyway to buy something that would connect to it to read the files?

The reason for this is, I have about 300 songs on there and a lot of photos and the music has been copied to a different folder from Filza. I am comfortable taking the phone apart, it actually is apart right now pretty much and I just need help reading the files of a dead iPhone.