Galaxy S4 won't turn on at all - the issue is apparently not the battery

I got an S4 mini from a friend, she said that it didn't turn on anymore. I thought it was an easy fix - just boot into recovery and wipe the system, then you're done - but it turns out I was wrong. (She told me she already was at a tech store and asked for a new battery, so that doesn't seem to be the problem.)

The phone is completely dead - it doesn't turn on at all, it doesn't get warm when charging, I cannot boot into recovery or safe mode, the "remove battery then press power button for a while"-trick also didn't work.

I'm out of ideas and didn't find anything new online. Any ideas?