iPhone 5S Power Issue

I’m not an iphone guy, so forgive me if this is stupid.

I am tinkering with a coworkers phone. It won’t boot by pressing the power button. However, if I plug it in, it will power on and go to recovery mode (I placed it in that mode).

I can’t get out of recovery mode. Doing a hard reset while its plugged in doesn’t seem to do anything. Doing it while it isn’t plugged in seems to power the device off, but when I power it back on (plugged in), it just goes back to recovery mode.

I tried using iTunes to upgrade iOS, but that failed. I don’t want to restore from a backup because that would lose any unbacked up data.

Any help would be appreciated.