Well, there are shops that do repairs for far less than Apple charges, and they often repair old gadgets that apple has ceased to support in any way. But considering the amount you will pay for labour plus parts, I recommend buying a used replacement on Ebay. Used 4s phones have become quite cheap, and putting a new battery in one is a fairly simple and non-technical procedure.
I would not under any circumstances recommend that you try to fix the screen yourself - with the 4s you have to disassemble the entire phone to get to the screen, and despite Ifixit’s propaganda, doing so is a task only to be undertaken by highly detail oriented people with sharp eyesight, fine motor control, technical acumen, and a lot of patience. Being a hobbit helps too.
ETA, once you have a replacement phone, sell your cracked one on Ebay for parts. You’ll get some cash back and save the old phone from becoming e-waste.
