How do I fix my iPhone 5 stuck on iTunes logo?

Hi! So I have an iPhone 5c, but two years ago it had a problem with the battery, and I was able to replace the battery few months ago. After replacing the battery, it was only showing the Apple logo, and now my iPhone got stuck on a screen that shows iTunes. I tried all kinds of solutions to get my iPhone back to work. None of them solved the problem. Also, my computer cannot recognize the phone. Do you know what I can do to solve this problem? I know the phone is too old, but I have important files on it. I don't have money to go to the repair shop. Tyia. 

Note: we were the one who changed it, and we never get it repaired to any repair shop.

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