iPhone 5c won't turn on no matter what

I was charging my iPhone 5c yesterday on a laptop and clicked on "don't trust this computer". I've done this before using the same laptop but this time my device's screen froze and the light faded a bit til it shut off completely. I turned it on again, but it kept happening every once in a while. I charged it overnight for about 5hours, it was fine til it shut down again and this time I couldn't turn it on anymore. I've tried doing reset and still nothing. I plugged it and held the power and home button til it lit up but no apple logo and it died again. I did the same thing and this time, the logo showed up but only for a second and it died again. What could be wrong 😟 I'm worried about my files. It was in the process of backing up. I bought it less than a month ago.