Help please, iPhone 6 data retrieval

Hello all, I have a broken iphone 6 and I would greatly appreciate any help. The screen was smashed and the phone stopped powering on. I took it to a local phone repair shop to replace the battery, fix the screen, and replace the camera (the repairs I thought that it needed) and they said that the phone has a short circuit in the logic board and they returned it to me as I initially brought the phone in to be fixed for use.

In current time, I just need the phone to get to a place that it will power on so that I'm able to retrieve my data, including many pictures and videos of my children that were not recently backed up to icloud.

When I currently plug the phone in it doesn't turn on, the phone just starts to feel warm and then hot. A hard reset also does nothing. I have only plugged it in for 15 minutes max at a time because of the heat and my lack of expertise. Should I try plugging the phone in for an hour and see if it will power on? I'm also going to get a new cord today because the shop said that it powered on while they were checking things but wasn't lasting. I'll probably go back within the next few days and ask more about that.

I do feel that the battery was compromised when the phone was smashed, but again the shop did not replace the phones battery or fix the broken screen as I brought the phone in to be fixed for use and so they didn't end up doing any of the repairs for the phone that I brought it in for because of the logic board short circuit issue.

Right now I just really want to focus on data retrieval and getting the phone to power on to enable that data retrieval. How should I best proceed next? Should I first replace the compromised battery? The smashed screen? I am currently looking into hiring a data retrieval expert and mailing the phone in as well but I want to make sure I'm doing what I can and that I'm moving in the right direction also.

Thank you very much for any help or advice 🙏