Looping logo iPhone 5c. Want to retrieve data!

Hello!

I just replaced the charging portfor my iPhone 5c. When I plugged everything back in I was pleased to see the Apple logo turn on, but it just kept turning off and turning back on. The iPhone was uncharged to begin with. Any thoughts on what to do to resolve this problem. There was no problem with the phone besides the fact that charging was difficult so this is all new.

At the very least I would like to retrieve my photos somewhere else as they are very important to me.

Thanks.