Curiously, my Fedora Linux Live USB is working just fine. It boots and everything. Didn't try to mount the NTFS partition on the SSD though. And it doesn't have drivers for the wifi, maybe cause it's an old version of the linux live distro I just had lying around. So, I couldn't test everything. But at least there's no problem with the RAM.
But we were not out of the woods yet... When we got to the step where you need to connect to a wifi network it didn't show any. Turns out it didn't have any drivers for the wifi card. That took some manual searching in the Microsoft update catalog:
With wifi drivers installed it was smooth sailing from there, and my partner now has a working computer again! πβ