Hello,
I am a certified apple repair agent working for geeks squad part time as an advanced repair agent. I think i can help answer your question. On all iphone models automated icloud back up is turned on by default. So unless that feature was turned off or your icloud storage was full you should be able to go to icloud.com and log in using your apple ID and password and see if your information was saved to icloud and can even download any photos, documents, or contact information directly from iCloud.com but as far as saving any information on the device itself if nothing was backed up prior to the logic board being damaged retreaving the data off of the device would be quite a difficult task and depending on what portion of the board was damaged might even be an impossible task. I hoped this helped answer your question and wish you the best of luck with solving this problem.