@Suiseiseki I know it isn't the kernel, the Caps Lock is responsive. I said 'Linux' as I do not know what exactly causes it to hang. I already tried disabling power saving stuff to no avail. HP's software is buggy, I have some experience of that already, so would be inclined to blame part of it on that.
I already tried Ctrl+Alt+F2 but it didn't work. So you know, this EliteBook does not have a SysRq key.
@Suiseiseki