Can the battery be replaced/will it be possible to retrieve photos?

My iPhone 4 battery completely died a month ago and cannot be recharged.  Not being tech savvy, I took for granted that my  phone’s setting were correct . I tried connecting with a new cable but that didn’t help.  I took it to the Apple Store, they connected it with a new cable and then offered their condolences.   I have since gotten a new iPhone, but my question is in two parts:  assuming a battery for an iPhone 4 could be located, can it be replaced?  I would not attempt it myself but would find an experienced professional to do it.  The second and more important part is what’s troubling me most because I may be thinking this is even possible when it isn’t.  Apparently the iCloud settings on my old phone were not on, and while pretty much everything else transferred over to my new phone (contacts, notes & a number of apps), my I’m-not-sure-how-many- years-of-photos did not.  IF a new battery could be installed correctly, would this allow the phone to be charged long enough for me to retrieve my photos (plus data from one or two games that I loved), or will that not work since my information from my old phone now exists on a new phone?  I don’t know if I’m thinking this through correctly so I wanted to ask more tech savvy people their thoughts before I spend $79 & ship it off to Apple.  I’d gladly spend ten times that amount if it will allow me to retrieve my photos, but I’m starting to think that maybe just replacing the battery may not be the answer.   I’ve stoically postponed my meltdown until I know for sure it’s a lost cause, but the pressure is really building up and I need to let it out.  Thanks in advance for any thoughts or suggestions.