My samsung galaxy s4 won't charge or turn on after i charged it.

I don't know what "flash the update" means.  A few days after Thanksgiving I was charging my Galaxy S4.  I had the power off so it would charge faster.  The first time I checked, the battery was almost 65%.  When I looked again, it was 88%.  I waited about 30 minutes for it to be fully charged.  It didn't turn on and hasn't since.  I am not sure of the operating system.  I got a new battery, have used different chargers, and have taken it to a cell phone repair center.  I was told if I could get another AT&T S4 he could just switch the data over.  Unfortunately, he wasn't able to do this.  This is the only place I have taken it because when I called my local AT&T store the guy I spoke to said it wouldn't be worth creating a ticket since the phone is "old and obsolete".  I informed him that I don't use the majority of it's capabilities, nor do I want anything bigger and won't fit in my purse or pocket.  I asked if he knew of any local repair shops (since he said it wasn't worth it).  He told me he was the manager and didn't know of any, but I was more than welcome to come in and ask for him.  He could help me find one I would enjoy.  I am willing to try ANYTHING to retrieve my data.  Actually just my texts.  My husband passed in April 2016,he was only 35.  I started taking screenshots of our conversations.  In Google Photo there are no screenshots of anything I ever took from different things.  I looked in all of the albums and tried using the search photos as well.  I apologize for the babbling!  PLEASE, PLEASE let me know if you have any other suggestions.  Thanks so much!